Alarmed at the chance that the Republican party might pick Rudolph Giuliani as its presidential nominee despite his support for abortion rights, a coalition of influential Christian conservatives is threatening to back a third-party candidate in an attempt to stop him.

The group making the threat, which came together Saturday in Salt Lake City during a break-away gathering during a meeting of the secretive Council for National Policy, includes Dr. James Dobson of Focus on the Family, who is perhaps the most influential of the group, as well as Tony Perkins of the Family Research Council, the direct mail pioneer Richard Viguerie and dozens of other politically-oriented conservative Christians, participants said. Almost everyone present expressed support for a written resolution that “if the Republican Party nominates a pro-abortion candidate we will consider running a third party candidate.”

The participants spoke on condition of anonymity because the both the Council for National Policy and the smaller meeting were secret, but they said members of the intend to publicize its resolution. These participants said the group chose the qualified term “consider” because they have not yet identified an alternative third party candidate, but the group was largely united in its plans to bolt the party if Mr. Giuliani became the candidate.

A revolt of Christian conservative leaders could be a significant setback to the Giuliani campaign because white evangelical Protestants make up a major portion of Republican primary voters. But the threat is risky for the credibility of the Christian conservative movement as well. Some of its usual grass-roots supporters could still choose to support even a pro-choice Republican like Mr. Giuliani, either because they dislike the Democratic nominee even more or because they are worried about war, terrorism and other issues.

In recent polls by the Pew Research Center, Mr. Giuliani has received a plurality of support from white evangelical Protestant voters despite a rising chorus of complaints from Christian conservative leaders about his liberal views on social issues and his unconventional family life. Some players in the movement not present at the meeting may be open to Mr. Giuliani as the lesser of two evils.

Rev. Pat Robertson’s Christian Broadcast Network, for example, has provided relatively generous coverage to Mr. Giuliani and his campaign. Gary Bauer, a Christian conservative political advocate and a Republican primary candidate eight years ago, said that, speaking by phone to the meeting, he urged the group to proceed with caution. “I can’t think of a bigger disaster for social conservatives, defense conservatives, and economic conservatives than Hillary Clinton in the White House,” Mr. Bauer said.

Still, he added, “But I do believe there are certain core issues for the Republican Party—low taxes, strong defense and pro life— and if we nominate some who is hostile on one of those three thing it will blow up the GOP.”

In response to the Christian conservatives, a spokeswoman for the Giuliani campaign provided a statement from Rep. Pete Sessions, a Texas Republican who supports Mr. Giuliani, saying, “Conservatives are rallying around the one candidate with the executive experience and proven leadership our country needs.” Calling Mr. Giuliani strong on fighting terrorism and “fiscal discipline,” Mr. Sessions said Republicans want a candidate who “can beat the Democratic nominee.”

For months, Christian conservatives have been escalating their warnings about the risk that nominating Mr. Giuliani could splinter the party. Dr. Dobson wrote a column declaring that he would waste his vote before casting it for either Mr. Giuliani or a Democrat who supports abortion rights like Senator Hillary Rodham Clinton. Richard Land, the top public policy official of the Southern Baptist Convention, has said that nominating a Republican candidate who supports abortion rights would make white evangelical votes “a jump ball” between the Republicans and Democrats, with other issues taking the fore.

Many Democrats, including Senator Clinton, are doing their best to soften the edges of their support for abortion rights, emphasizing they favor policies that might reduce the number of unwanted pregnancies.

But participants in the group that endorsed the resolution said they reached their position hearing an assessment of the state of the Republican primary from Mr. Perkins, who acts as a point man in Washington for the movement. Mr. Perkins told them that Mr. Giuliani could plausibly win the primary if he carried Florida, which is also a state with many conservative Christian voters, and now was the best-chance to stop any momentum behind the campaign.