While professing a common ground on the issue of property taxes, Governor Paterson and Senator Dean Skelos emerged from their first formal meeting since the latter was anointed majority leader without an agreement on how to slow down the rapid growth in local school tax levies.

Saying he had a “productive discussion” with the governor, Mr. Skelos, a Long Island legislator who succeeded Senator Joseph Bruno last week as the state’s top Republican, expressed hope that lawmakers and the governor would “come to a resolution” on a property tax cap plan as early as this month.

He declined, however, to fully endorse Mr. Paterson’s proposal to impose a 4% cap on annual property tax growth in suburban and rural school districts. “If a cap is part of the solution, then I will be supportive of a cap,” Mr. Skelos said.

Mr. Paterson, a Democrat, said he wouldn’t call the Legislature back to Albany for a special session unless he and lawmakers moved closer to a deal. “I’m not going to do it in a coercive way,” he said.

Despite the lack of resolution, the two leaders, who are both new to their jobs, made a show of friendship in what was a rare occasion in Albany: a sitting governor staging a press conference exclusively with a leader from a rival party.

Mr. Paterson noted that he and Mr. Skelos for several years served together as deputy leaders in their respective conferences, and that he spent his childhood in Hempstead, just north of Mr. Skelos’s hometown of Rockville Centre.

“The governor and I have a very cordial, noncombative relationship,” Mr. Skelos said, complimenting the governor on his “bold leadership.”

The leaders have an incentive to get along. Mr. Skelos, whose hard-edged style has led Senate Democrats to nickname him “Mean Dean,” is reaching out to the governor with the hope that Mr. Paterson will stay on the sidelines during the fall election season and limit his assistance to Senate Democrats, who are within striking distance of seizing a majority.

Messrs. Paterson and Bruno flaunted their affinity for each other. Mr. Bruno’s departure raised the question of whether the goodwill would extend to Mr. Skelos, a leader more accustomed to political warfare.

As governor, Mr. Paterson has pointedly tried to distinguish himself from his predecessor, Eliot Spitzer, by showering lawmakers with praise and affection without regard to party affiliation.

Still, Mr. Paterson is relying on Senate Republicans for cooperation on what has become the signature issue of his young governorship: The governor is counting on Republican support for a property tax cap to build pressure on Assembly Democrats, who are more resistant to the idea, to negotiate legislation.

Mr. Paterson’s rapport with Senate Republicans has raised some eyebrows among Senate Democrats, who question whether his outreach is traipsing into the territory of political alliance.

The two leaders held a press conference after meeting for an hour in the governor’s Manhattan office suite. Earlier in the day, Mr. Skelos met with Mayor Bloomberg at the Sheraton New York, their first sit-down meeting since the senator became majority leader.

Mr. Skelos offered few details about his discussions with the mayor, who has contributed hundreds of thousands of dollars to Senate Republicans in recent years. “He did not ask for any commitments on anything,” he said of the mayor. “He expressed his friendship and, hopefully, his continued support.”

Mr. Bloomberg’s resources could become even more important should another billionaire businessman pour money into the legislative contests.

Rochester entrepreneur Thomas Golisano, who spent nearly $100 million of his fortune on three unsuccessful independent bids for governor, will announce the formation of a political action committee next week, according to a report yesterday by the Capitol newspaper.

The newspaper said Mr. Golisano, a maverick Republican who was one of Governor Pataki’s most persistent critics, is considering bankrolling Democratic candidates competing for Senate seats in Erie County.