ALBANY — The state Capitol’s “three men in a room” added its newest member Sunday, but they left their hour-long huddle at the governor’s mansion without compromise on critical issues facing taxpayers.

Senate Majority Leader Dean Skelos, R-Suffolk County, pushed for a school property-tax cap in his first behind-closed-doors meeting with Assembly Speaker Sheldon Silver, D-Manhattan, and Gov. David Paterson — who together make up the most powerful, and often most criticized, group in state government.

Silver reiterated his concerns that a property-tax cap, which under Paterson’s proposal would limit the growth in school taxes to 4 percent a year, could hurt aid to education.

“What guarantees do we have that the children in those school districts will continue to get the resources that are necessary when they graduate to become competitive members” of society, Silver asked as the leaders briefed reporters on the mansion’s front porch after the meeting.

Skelos said his Senate conference, which is clinging to a 31-30 seat majority in the chamber, will return to Albany within a month to approve Paterson’s plan.

Since taking the helm of the Senate Republicans last month after the resignation of former Majority Leader Joseph Bruno, Skelos has backed away from Bruno’s reservations about a cap and has supported it as a first step in curbing the state’s high property taxes.

“I know there are some disagreements on how we move forward with real property-tax relief, but I believe we can accomplish it,” Skelos said.

Tax relief was one of several issues the men said they discussed during the rare, out-of-session leaders’ meeting. Though its members have changed over the years, the group has been knocked for making important decisions in secret and without public input.

But Paterson said he wants to keep discussions going with the leaders, despite the state Legislature being on summer break.

Rank-and-file lawmakers left Albany last month to campaign for the critical November elections, when all 212 seats in the Legislature are up for election.

The leaders said they talked about trying to help homeowners this winter with rising home-heating prices and picking a firm to operate video-lottery terminals at Aqueduct Racetrack in Queens.

Additionally, Paterson said he warned the group the state’s revenue is expected to dwindle during the current 2008-09 fiscal year because of Wall Street’s woes.

But he stopped short of saying he would call the Legislature back to make budget cuts during the fiscal year, which runs until March 31. He is meeting with his cabinet Monday to discuss the need to trim state spending.

Finding a way to lower property taxes, though, may be most elusive issue facing lawmakers. Striking a deal before the November elections could be a boost to help Republicans, who largely represent upstate and Long Island areas stun by high taxes, stay in power in the Senate.

To that end, Skelos said he will bring the Senate back to vote on a cap, even without a deal with the Assembly, to send a signal about their commitment to the idea.

Paterson, a Democrat who took office in March from disgraced Gov. Eliot Spitzer and has focused on getting bi-partisan cooperation, applauded Skelos for supporting a cap.

Yet Paterson recognized that the gesture would mean nothing unless he can broker a compromise between Silver and Skelos.

“I’m not going to drag people in for some kind of demonstration that I can actually” bring the Legislature into session, Paterson said. “I really want results, and when we think we are at a point that we are likely to succeed, we’re willing to come back in.”

Reach Joseph spector at jspector@gannett.com.