ALBANY – The battle over school choice in New York escalated yesterday, as Cardinal Egan and thousands of schoolchildren, parents, and teachers rallied here to pressure lawmakers to back a plan by Governor Pataki that would give tuition tax credits to parents with children in failing schools.

Efforts are also under way by critics of the governor’s plan to condition support for the tax credits on Albany’s compliance with a public school-financing lawsuit. A powerful opponent of the tax credit plan, the president of the United Federation of Teachers, is signaling to Catholic leaders that she might be flexible on the issue of tax credits, but is urging them to support her demands that Albany spend billions of more dollars on New York City public schools.

The connection between the two issues was also drawn by the Democratic speaker of the Assembly, Sheldon Silver, who said yesterday that he wouldn’t rule out supporting the governor’s plan, but that any decision would be made “within the confines of making sure that we take care of public education.”

Mr. Pataki wants New York to join a handful of other states that offer so-called “education tax credits” to parents. Under the governor’s plan, low- to-middle-income parents of public and private schoolchildren in struggling school districts would be eligible to receive up to $500 in tax credits, which reduce tax liability dollar for dollar, to help pay for private school tuition or tutoring.

While the governor’s office estimates that 80% of the $400 million program would assist public school parents, critics of the plan, particularly the teachers union, fear that it would open the door to tuition vouchers and would ultimately siphon money away from the public school system, and thus teachers.

But there’s a sense that the union might warm up to the plan if Senate Republicans and Mr. Pataki moved toward complying with a court ruling in the Campaign for Fiscal Equity case that requires the state to spend an additional $23 billion over five years on city schools to ensure that the schools deliver a “sound basic” education, which the court has found to be a requirement under the state constitution.

In an interview with The New York Sun, the leader of the diocese of Brooklyn, Bishop Nicholas DiMarzio, said the president of the UFT, Randi Weingarten, told him during a one-hour meeting on Monday that she “has an evolving position” on tuition tax credits. Without support from the UFT, a dominant interest group in Albany, Assembly Democrats are unlikely to approve the governor’s plan.

Ms. Weingarten, who proposed the meeting, said she and the bishop “explored each other’s positions” and described the conversation as “wide-ranging” and “cordial.” She said she told “him how important it was to help all students in New York City get a decent education” and said he “should support our efforts to get CFE money,” referring to the court ruling, which the governor’s office has appealed. She said she didn’t “tie” the two issues together.

Bishop DiMarzio, who said he fears for the survival of Catholic schools in Brooklyn and Queens, called the CFE case and the governor’s tax credit plan “two separate issues,” saying, “They really are very different. One is in court, and this is a possibility now.” He said Ms. Weingarten “wants what she thinks is important for the schools she’s responsible for, and we know what’s important for ours.”

An estimated 3,000 people thronged the steps of the State Capitol Building and the surrounding grounds, mostly schoolchildren of parochial schools primarily from Manhattan, Brooklyn, Queens, Long Island, Rochester, and Syracuse. Most of the participants came to Albany on buses paid for by their schools and Teach NYS, a recently established lobbying group backed by Jewish and Catholic philanthropists that organized the event. The students, who were shivering in their winter coats, chanted “save our schools,” while a phalanx of politicians and religions leaders stood on a podium, taking turns addressing the crowd.

“We’re talking about giving the middle class and working class the kind of opportunities that the wealthy have,” Cardinal Egan, the archbishop of New York, told the gathering, according to the Associated Press.

Traveling with her students from Flushing, Queens, Rachel Reifer, the principal of Shevach High School, said she supported the governor’s plan because it’s “really a burden for people to pay school taxes, and in addition, they have to pay school tuition, which can really sometimes be exorbitant for many families.” Tuition at the Jewish school is $8,000.

Following the rally, Cardinal Egan, Bishop DiMarzio, and three New York rabbis held meetings with Mr. Pataki, Joseph Bruno, the Republican majority leader of the Senate, and Mr. Silver, who is an Orthodox Jew and represents a district in Lower Manhattan. Before his meeting, Mr. Silver said yesterday to reporters that he was concerned about the cost of the governor’s plan.

Speaking to reporters after speaking at the rally, Mr. Pataki dismissed the notion that the state couldn’t afford the tax credits. “We are providing $17 billion for public education this year in our budget,” he said. “I certainly think we can find $500 to help a parent with a child in a failing school.”