Pro-union supporters celebrate as Scottish independence referendum results are announced in Glasgow, Scotland. AFP/Getty Images

EDINBURGH—Scottish voters rejected a heated bid for independence, providing a narrow escape for a British government that scrambled to dole out promises of new local powers for Edinburgh to head off the breakup of a 307-year-old union.

Scotland's First Minister Alex Salmond conceded early Friday that Scotland had voted to stay within the U.K. Photo: Getty Images

Scottish First Minister Alex Salmond said early Friday he had accepted that the majority of Scottish voters had decided not to become an independent country.

The tally at around 6:30 a.m. local time, which included results from 31 of the 32 districts in Scotland, showed 55% of voters rejecting the independence question and 45% favoring it. About 3.5 million votes had been counted. More than four million people were registered to vote in the election.

Mr. Salmond said the fact that around 1.6 million people voted to exit the union was a victory in itself. "I don't think of any of us…would have thought such a thing could be credible or possible," he said.

While the pro-independence camp won expected victories in places like Glasgow and Dundee, the U.K. government's late press to pull out a victory appeared to help avert a major embarrassment. The outcome is a relief for British Prime Minister David Cameron, who agreed to the referendum in a deal two years ago with Mr. Salmond, then watched as a double-digit lead dissolved to a dead heat on the back of relentless campaigning by Mr. Salmond and the pro-independence campaign.

Mr. Cameron said Friday morning that he would honor his commitment to devolve more powers to Scotland's semi-autonomous government, but also said England, Wales, and Northern Ireland should also have a greater independence in how they govern their affairs.

The prime minister said work would begin to grant the devolved government of Scotland more control over tax, spending, and welfare, with a view to forming plans by November and draft legislation published by January.

Mr. Cameron sldo congratulated Alistair Darling, the Labour politician who helped spearhead the "no" camp, on a "well-fought campaign" in a message from his official Twitter account.

"Today is a momentous result for Scotland and also for the United Kingdom as a whole," said Mr. Darling. But he also acknowledge the large numbers that had voted for independence. "Every political party must now listen to their cry for change," he said, in a speech as the results were announced Friday morning U.K. time.

The late surge to reject the independence movement was fueled in part by pledges of new powers that would bring more self-rule to Scotland. But the government also issued tough warnings that Scotland's economy would suffer if it escaped the U.K.'s embrace.

Market Talk

Scotland 'No' Boosts Spanish Bonds The relief following the rejection of independence by Scottish voters isn't only being felt in U.K. assets. Spanish bonds have made early gains, reversing some of the weakness seen in recent weeks as investors worried that surging support for a Scottish breakaway could encourage separatists in Catalonia, due to hold their own referendum in November—albeit without Madrid's blessing. Spanish 10-year bond yields are down 0.06 percentage point at 2.22%, with Italian bonds also benefitting. Still, the Scottish-inspired relief rally is likely to be short-lived, according to UBS strategist Justin Knight. "After this, the impact on Spanish yield spreads stemming from the Catalan situation will, we think, be the result of developments within Spain only," he says. (tommy.stubbington@wsj.com)

Market Talk is a stream of real-time news and market analysis that is available on Dow Jones Newswires

The financial markets expressed relief. The "no" vote "removes the huge political and economic uncertainty of untangling the 307-year-old union," said HSBC analyst Simon Wells in a research note Friday morning. "The downside risk to UK growth has lifted and we think it keeps the (Bank of England) on track to raise rates in February next year."

A key factor in interpreting the results early Friday was voter turnout, which was high across the country following a campaign that consumed Scotland—but lower in some places that would be expected to support breaking away from the U.K.

Mark Diffley, research director at pollster Ipsos-Mori, said the win for the "no" campaign came to down to high voter turnout in areas that tended to support staying with the U.K. At the same time, areas with higher support for independence, such as Glasgow and Dundee, had relatively low voter turnout. Turnout in Glasgow was 75%, which is low compared with other districts that saw turnout above 90%.

"It's turnout that's crucial," Mr. Diffley said. He also said that in a referendum that involves change vs. staying the same, the status quo option will tend to do better at the polls than is predicted immediately before.

Currency markets were clearly intuiting that the independence movement would be defeated, with the pound strengthening steadily against the dollar in overnight hours.

Nicola Sturgeon, deputy leader of the pro-independence Scottish National Party, told the BBC that she was "deeply disappointed" that her party appears to have lost. She added that although the pro-U.K. camp was in the lead, more than one million Scots had voted for independence.

"What we are not seeing, emphatically not, is any kind of endorsement of the status quo," she said.

Glasgow, Scotland's biggest city, backed independence by 53% to 47%. The "yes" camp also won Dundee, an industrial town on Scotland's east coast and the districts of North Lanarkshire and West Dunbartonshire.

"I am totally heartbroken," said Heather McGuire as she cried in Glasgow's central square with a Scottish flag round her neck. "But at the end of the day I am still Scottish," she said, kissing the flag.

Early results from the islands in Scotland's north, where much of the oil flows, came in strongly for staying in the union.

Another blow for the "yes" camp was its failure to win Inverclyde, a working-class district that left-wing independence supporters had hoped to win.

Brian Robertson, a pro-independence member of the largely pro-union Labour Party, said losing Inverclyde was "a big disappointment." The results showed so far that pro-independence campaigners had not been as successful as they had hoped in poorer areas, such as Invercylde.

Aberdeen, the hub of Scotland's oil industry, voted in favor of staying in the U.K.

It was an emotional day in Scotland, where voters turned out in droves to make what was among the biggest political decisions of their lives. The ballot asked a simple question—"Should Scotland be an independent country?"

Boisterous crowds gathered in the streets of Glasgow and elsewhere, waving the blue Scottish Saltire flag. Some people played bagpipes, some wore kilts.

Carrying a Scottish flag in the center of Glasgow, independence supporter Kyle McBride, 21, braced for a "No" vote. "My heart says yes but my head says no," he said. "The polls were too much for us this time." But the student said he expects there would be another chance to go for independence. "The 'Yes' campaign has absolutely rocked it. This may not be the time, but it is going to happen."

In Edinburgh, 26-year-old job seeker Ian Drummond voted "No." "I believe we are united together. We have more in common than differences," he said. "I love haggis, Irn-Bru [an orange-colored carbonated soft drink] and I have a kilt at home but this is not enough for a messy divorce from the English."

Mr. Salmond, leader of the Scottish National Party and the central figure in the diverse, grass-roots pro-independence campaign, had urged Scots to take the plunge, saying the nation would be richer and happier if it breaks away from the U.K.

But Mr. Cameron and other senior politicians spent the past two weeks in frantic dashes between Scotland and England to shore up support for the union. They have tried to persuade Scots that independence is fraught with economic risks that would endanger advocates' vision of a Scottish government with a freer hand to intervene to lower poverty and reduce inequality.

In an effort to woo voters eager for greater autonomy but wary of quitting the U.K., London has pledged to transfer more power over tax and spending to Scotland's semiautonomous parliament in Edinburgh.

The measures were laid out after polls suggested the "yes" campaign was gaining momentum. Some voters said they felt insulted that U.K. politicians didn't seem to have taken the referendum seriously until the last minute.

Roy Hogg, a 51-year-old hotel concierge, said he is happy U.K. politicians offered more powers to the Scottish government in recent weeks and he thinks the offer is genuine, but he still wasn't impressed.

"Westminster is broken and detached from the Scottish people," he said.

Young people are playing a larger-than-usual role in the vote, with everyone aged 16 or over eligible to vote in the referendum, even though the age requirement in general elections is usually 18 years.

The referendum brought to the surface strong feelings on both sides of the debate. Anne Law, 46, walked away from a polling station at a primary school in Glasgow with tears in her eyes.

"I feel quite emotional now," Ms. Law said. She then drove away, with a Scottish flag flying from the roof of her car.

—Cassie Werber and Max Colchester contributed to this article.

Write to Jason Douglas at jason.douglas@wsj.com, Jenny Gross at jenny.gross@wsj.com and Chiara Albanese at chiara.albanese@wsj.com