The city and state have moved to dismiss a challenge to the city's property-tax system by black and Hispanic renters. The plaintiffs contend that rental buildings are taxed at higher rates than co-ops, condos and private houses, which are more likely to be occupied by whites.

In separate filings, the city and state said changes to the property-tax assessment system were best carried out by the legislature, rather than the courts, even if the tax system "is not immune from criticism," as noted in the city's brief, filed Monday. The briefs argued that the renters, who didn't directly pay property taxes, lacked standing to bring a court challenge. The state filed its motion Friday.

The suit seeks to throw out much of the city's $20 billion property-tax system. Lucas Ferrara, of Newman Ferrara LLP, which filed the suit in February, said the city and state had "opted to play procedural games."

The motion is due to be heard in October in state Supreme Court in Manhattan.

Write to Josh Barbanel at josh.barbanel@wsj.com