ALBANY – Gov. Andrew M. Cuomo’s seven-round limit on magazines sold in New York will be suspended “indefinitely” by a measure in his $136.5 billion budget set to be passed this week, said Dean Skelos, a State Senate majority leader, said.

The ban on magazines holding more than seven bullets was set to start April 15. Cuomo has said the law needs to be rolled back because manufacturers don’t make seven-round holders. The measure was a centerpiece to a gun law the 55-year-old Democratic governor pushed through the Legislature in January, making New York the first state to respond with tougher gun regulations to the elementary school massacre in Newtown, Conn.

The budget “bill will have an indefinite postponement of the issue,” Skelos, the Long Island Republican who co-leads the Senate with a group of five breakaway Democrats, told reporters in Albany on Sunday.

Josh Vlasto, a Cuomo spokesman, didn’t respond to an email requesting comment.

The suspension means magazines holding up to 10 rounds will continue to be sold. Other pieces of Cuomo’s gun law, including measures that close loopholes in a 2000 assault weapons ban that Cuomo said had more holes than Swiss cheese and tougher background checks for sales, won’t be touched by the changes. The governor began pressing for tighter firearm controls after 20 children and six adults were gunned down at Sandy Hook Elementary School in Newtown on Dec. 14.

Cuomo has been criticized by pro-gun groups, including the National Rifle Association, for waiving a requirement that bills sit for three days before they’re passed. His gun law was passed within 24 hours of being introduced, a move Cuomo has said was necessary to prevent a sales rush on assault weapons.

Cuomo and the Legislature had once predicted the budget would be final March 21, but policy issues bogged down talks. Instead of passing an extraordinarily early budget as they planned, lawmakers are now rushing to meet the April 1 deadline a few days early. The Senate is scheduled to meet through Wednesday. The Assembly will return to Albany on Thursday to begin voting. Several religious holidays in the coming week, including Passover and Easter, have complicated scheduling.

In a rare Sunday session, State Senate lawmakers began advancing legislation.

The deal on the voting schedule was struck last week, but voluminous budget bills that in total are several feet thick had to be printed, and several policy issues, such as proposed restrictions on the New York Police Department’s stop-and-frisk policy, were inserted, then extracted from, the 2013-14 budget as those talks delayed agreements.

State Sen. John DeFrancisco, a Syracuse Republican, said lawmakers hoped to have the rest printed by midnight Sunday.

Sunday, the State Senate began advancing measures for public protection, transportation and economic development.

DeFrancisco said Western New York should be pleased with the budget’s economic development boosts, including funds to help keep the Buffalo Bills in Ralph Wilson Stadium.

Cuomo has said the budget holds spending increases under 2 percent in what would be a third consecutive on-time annual spending plan.

Though billed as not raising taxes, it is built on revenues from extending two taxes – one on millionaires and another on corporate energy bills – that were due to expire. Annual increases in public college tuition also would continue.

The agreement includes increasing the minimum wage to $8 on Jan. 1, $8.75 a year later and $9 a year after that. The current minimum wage is $7.25.

State Sen. Kevin Parker, a Brooklyn Democrat, said the wages are too low and that the $9 wage will be obsolete before it gets there.

The budget also calls for $350 tax rebate checks to be sent to New Yorkers in 2014, an election year. The checks will go to households with at least one child and an income of $40,000 to $300,000. Critics have called the move a political gimmick designed only to aid incumbents on Election Day.

Bloomberg News and the Associated Press contributed to this report.