PITTSBURGH — United Methodist evangelicals said Thursday that their church should split after three decades of discord over homosexuality, signaling a deep rift in the nation's third-largest denomination.

Their proposal, at the Methodist national policy meeting, reflected widespread frustration that years of debate over gay-related issues have diverted the 8.3 million-member church from its broader mission.

"We can't bridge the gap separating us," said the Rev. William Hinson, former pastor of First United Methodist Church of Houston and president of the Confessing Movement for conservative Methodists. "Our people, who have been faithful and patient, should not have to endure our endless conflict."

No schism is imminent. A breakup would involve complex negotiations over billions of dollars in assets and the 36,000 congregations in the United States alone. Church law prevents any congregation from walking away with Methodist property.

The move also would likely be opposed by the many Methodists for whom homosexuality is not a central concern, church observers say. And Hinson said that some evangelicals do not yet support the plan.

However, he and other conservatives said that they would continue to pursue the idea even if delegates to this week's General Conference reject a proposal to form a task force to study it. The meeting ends Friday.

"Both sides are so terribly divided in our denomination," said the Rev. James Heidinger, leader of the Methodist evangelical group Good News.

"We might find a way to be in ministry according to our own convictions and consciences without the continued internecine battling that goes on."

The announcement came after conservatives prevailed at the meeting in maintaining the church's firm stand against homosexuality.

Delegates affirmed that gay sex was "incompatible with Christian teaching" and made it a chargeable offense under church law for clergy to conduct same-sex marriages and for unmarried ministers to have sex.

However, evangelicals expect that those who want a broader role for gays and lesbians in the church will continue to defy church law and appoint sexually active homosexual clergy.

More than 200 people protested the denomination's prohibition against gay sex by disrupting the Thursday morning session. Demonstrators walked onto the floor and the stage where church officials were directing the debate, singing hymns and waiving rainbow streamers and posters for about 20 minutes. Some wept.

Dozens of delegates and bishops stood up in a sign of solidarity with the protesters before business resumed.