Mayor Bill de Blasio Tuesday backed the latest bill in Albany to let New York City set its own speed limit.

The administration sent a letter of support for the legislation from state Sen. Jeff Klein of the Bronx introduced days before the legislative session ends on Thursday.

"We have seen real movement over the past 24 hours," said Wiley Norvell, an administration spokesman. "We are very hopeful that we'll have action this session that empowers New York City to curb dangerous speeds on our streets and better protect our communities."

The bill introduced Monday night from Klein, leader of the Independent Democratic Conference that shares power with Republicans, was a compromise on a key issue in de Blasio's "Vision Zero" street safety initiative. Klein's bill would let the city cut the default speed limit to 25 mph from 30 mph and require local community boards to weigh in on any changes to slow traffic on a street by more than 5 mph, though the Department of Transportation gets the final say.

"Our community boards are on the front lines of local concerns each and every day and know their streets best, which is why they deserve to have a voice in this process," Klein said in a statement.

The bill differs from one in the state Assembly that would not require community board input for cutting the speed limit or traffic-calming measures to limit drivers to 20 mph on residential streets -- two measures that one street safety group, Right of Way, felt would bog down de Blasio's Vision Zero effort.

"Both provisions are a slap in the face to grieving families and indeed the whole livable streets community," said Right of Way's Keegan Stephan in a statement.

The details of Klein's bill were hashed out with the city, according to an IDC source. Assemblyman Daniel O'Donnell, who had pushed his own speed limit bill, touted his version over Klein's legislation. Nonetheless, O'Donnell is confident that one of the versions will pass.

"I expect both houses to vote on one or the other at the end of the week," O'Donnell said.

Meanwhile, Transportation Alternatives and Families for Safe Streets endorsed the legislation, which must pass by Thursday.

"We can't wait until next year to take action," Transportation Alternatives executive director Paul Steely White said in a statement. "Speeding remains the number one cause of fatal crashes, killing more New Yorkers than drunk driving and distracted driving combined."