By Laila Kearney

SAN FRANCISCO, March 15 (Reuters) - Former U.S. Secretary of State Condoleezza Rice on Saturday called on the Republican Party to become more inclusive on issues like immigration.

"We have a responsibility to those who do not yet have the liberties and the rights that we enjoy," Rice told a cheering crowd at the annual gathering of California Republicans in the San Francisco suburb of Burlingame. "We cannot abandon them ... We were once them."

She did not offer a specific policy idea.

The speech by Rice, who was secretary of state under President George W. Bush, was the highlight of the second day of the three-day convention, which has set out to rebuild the party in a state where Democrats control both houses of the legislature and every statewide elected office.

U.S. Representative Pete Sessions of Texas, who recently won a primary battle against a challenger from the populist Tea Party movement, also talked about broadening the Republican Party by joining in a fight with the Tea Party against Democrats and liberals.

"The opportunities that lie for Republicans are enormous this year with a team that will be together," Sessions said. "It's easier to get things done in a majority."

Jim Brulte, California's former and long-serving state senate leader who has been charged with reviving the party in the state, said in a statement he was aiming to push the party "outside of its comfort zone."

In her speech, Rice echoed the convention theme of "rebuild, renew and reclaim." Rice included individual freedom, private sector-led growth and equal access to quality education as key themes for Republicans to focus on in California and elsewhere.

Convention attendees said they were behind the idea of Republicans reaching out to groups that have traditionally felt alienated by the party, particularly Latino and Asian immigrants.

"I really think that this country is going to be turned around with conservatives and new immigrants," said Susan Mason, of Sacramento, a Tea Party Republican. "We've got to get to them first." (Editing by Edith Honan and Paul Simao)