New York State Gov. Andrew Cuomo, left, and Former Massachusetts Gov. and GOP presidential candidate Mitt Romney, right Associated Press, left, and Getty Images, right

Mitt Romney on Monday issued a fundraising appeal for New York gubernatorial candidate Rob Astorino, calling Gov. Andrew Cuomo “a typical corrupt New York politician.”

The 2012 GOP presidential nominee has joined the ranks of other prominent Republican figures, including former Florida Gov. Jeb Bush and Texas Gov. Rick Perry, in supporting Mr. Astorino’s struggling candidacy—in notable contrast to New Jersey Gov. Chris Christie.

“The difference between Andrew Cuomo and Rob Astorino is astounding,” Mr. Romney wrote in a letter distributed Monday to prospective Astorino campaign donors.

“Mr. Cuomo, a typical corrupt New York politician, is trying to sell his story that ‘New York is open for business’ by using millions of taxpayer dollars to fund his ludicrous Start-Up New York campaign,” he wrote, referring to a Cuomo administration economic-development program.

The governor dismissed Mr. Romney’s remarks.

“New Yorkers have already commented on Mitt Romney’s positions and made it abundantly clear that his theory has been rejected in the state,” Mr. Cuomo said Monday while speaking to reporters before marching in the Columbus Day parade in Midtown.

In 2012, when Mr. Romney was the GOP presidential nominee, he lost New York state, earning 36% of the vote to President Barack Obama ’s 63%.

While Mr. Romney and others have come out for Mr. Astorino, Mr. Christie, the chairman of the Republican Governors Association, has dismissed the New York race, calling it a lost cause.

The association has declined to provide a financial lifeline to Mr. Astorino’s campaign, which has been pummeled by millions of dollars of advertising on behalf of Mr. Cuomo.

As of the most recent filings with the state Board of Elections, Mr. Astorino’s campaign has nearly $1.3 million in cash on hand, while Mr. Cuomo, a Democrat, sits on $23.7 million.

Write to Erica Orden at erica.orden@wsj.com