ALBANY — Senate Republicans went on the offensive in the fight over soon-to-expire rent laws yesterday, advancing a bill to let landlords deregulate thousands of units, including many in Stuyvesant Town and Peter Cooper Village.

The one-house legislation holds little hope for passage, but was widely seen as a shot across the bow at Democrats, who are desperate to renew — and greatly expand — tenant protections before regulations on 1 million city units expire June 15.

The bill would allow landlords to repay the city tens of millions of dollars in special tax breaks in exchange for removing up to 37,000 apartments from the rent-stabilization program.Senate Democrats protested the bill, which they said sought to circumvent a decision by the state’s highest court.