ALBANY – Opponents of legalized abortion are asking Senator Clinton to put her meeting where her mouth is, after a speech in which the former first lady said people on both sides of the hot-button issue should work to find “common ground.”

In a speech last month to Family Planning Advocates of New York State, Mrs. Clinton reiterated her view that emergency contraception and legal abortion should be widely available to women in America and abroad. She recommended lifting what is known as the Mexico City Policy, which forbids giving federal funds to American organizations that provide abortions overseas. And she called for establishing a first-ever nationwide sex-education program.

Political observers keyed in, however, on moments in the speech where Mrs. Clinton appeared to be softening her position on abortion.

According to news reports, audience members gasped when New York’s junior senator said she “respects those who believe with all their hearts and minds that there are no circumstances under which any abortion should ever be available.” Mrs. Clinton also raised eyebrows by telling supporters to “embrace” research showing that religious and moral values are a strong deterrent to teenage sex.

Mrs. Clinton is widely expected to run for president in 2008, but she has not publicly stated whether she will. Her comments on abortion got widespread attention because a move toward the center is thought to be key to for her to achieve national office. Mrs. Clinton’s husband won two terms in the White House by using a similar strategy, and political observers have cited the liberal tag as fatal to the candidacies of Senator Kerry last year and Vice President Gore in 2000.

“Finding the political center is certainly something Bill Clinton has been a master at,” a professor of public policy at Columbia University, Steven Cohen, said. “And it’s obvious that Hillary has benefited from her experience with him.”

Testing Mrs. Clinton’s claims, however, are a collection of advocacy groups opposed to abortion. The president of the Christian Defense Coalition, Patrick Mahoney, issued a letter to the senator’s office Wednesday requesting that she meet with opponents of abortion to discuss possible areas where common ground could be found.

A spokeswoman for Mrs. Clinton, Amy Bonitatibus, said one of the senator’s legislative aides met privately with Mr. Mahoney and relayed the request for a meeting to Mrs. Clinton’s schedulers.

“They were professional,” Mr. Mahoney said. “If we don’t hear by the end of next week we will go up to her office until we hear a yes or a no.”

Mr. Mahoney, a Presbyterian minister, said he represents a coalition that includes the Staten Island-based group Priests for Life, the National Clergy Council, Generation Life, and Silent No More, and his own Christian Defense Council. He said his goal is for Mrs. Clinton to reverse her opposition to a federal ban on partial-birth abortions, to secure financing for a study on the psychological and physical effects of abortion on women who have had them, and to support federal abstinence programs.

“If she declines a meeting with the pro-life community after talking about common ground, then I think she’s using political rhetoric and is not sincere,” Mr. Mahoney said. “But we couldn’t let the comments go without holding the senator to some sense of accountability.”

Recent polls showed Mrs. Clinton gaining in popularity among New York voters, even before her comments on abortion late last month.

A Quinnipiac University poll released this week said the senator would thump Governor Pataki and edge out Mayor Giuliani in hypothetical matchups for the U.S. Senate. Neither Republican has indicated he plans to run against her next year. Most respondents, or 82%, said they had heard “nothing or little” about Mrs. Clinton’s recent comments on abortion.

According to the same Quinnipiac poll, New Yorkers are split on whether Mrs. Clinton should run for president in 2008. Democratic respondents favor Clinton campaign for the White House, 67% to 27%.

The poll also found Mrs. Clinton’s popularity among state residents at an all-time high of 65%.

Mr. Cohen at Columbia attributed that, in part, to her efforts at centrism.

“The Clintons are basically New Democrats,” he said. “And the New Democrats are basically about trying to find ways to find the center.”

That strategy may be more effective, however, for Democrats than for Republicans.

According to another Quinnipiac University poll this week, Mr. Pataki’s approval rating among state residents has spiraled from 44% in December to an all-time low of 34%. Mr. Pataki has not said whether he plans to seek another term in office, but early polls show him trailing by a considerable margin the attorney general, Eliot Spitzer.

The poll numbers on Mrs. Clinton are significant because she entered the Senate race four years ago being criticized because she had never previously been a New York resident and potentially tarnished by the impeachment of her husband. Early on, Mrs. Clinton was thought to be an underdog against Mr. Giuliani, who eventually backed out of the race after discovering he had prostate cancer.

But the Quinnipiac poll said 64% of New Yorkers now believe Mrs. Clinton is trustworthy and concerned about the issues that affect them.

“Remember when Senator Clinton took office four years ago,” the poll’s director, Maurice Carroll, said. “Her husband had just pardoned Marc Rich and the Clintons were accused of looting the White House furniture. Now, two thirds of New Yorkers say she’s a good – and honest – senator.”