Weathering weeks of scrutiny in his campaign for governor about his views on women, Arnold Schwarzenegger positioned himself Tuesday as a respectful husband committed to restoring women’s faith in the California Republican Party.

“One of the biggest mistakes the Republican Party has made is they haven’t reached out enough to women,” Schwarzenegger told a group of about 150 supporters at a town hall meeting in Sacramento. “You have to include women much more, to bring them to the table, make them really part of the party.”

More than a million women abandoned the party in recent years, Schwarzenegger said. “We have to bring them back. … I think that I can do that.”

The actor and first-time candidate — whose campaign stumbled recently over his own past accounts of sexual escapades as a professional bodybuilder decades ago — didn’t offer specifics on how the GOP could attract women during the question-and-answer session at the Sheraton Grand Hotel. He already has said he supports abortion rights but wants parental consent laws for underage girls and opposes late-term abortions.

Beyond their stances on abortion rights, the major candidates in the crowded, two-month race to unseat and replace Gov. Gray Davis in the Oct. 7 recall election have not placed an emphasis on women’s issues.

In a race driven largely by voters’ discontent over California’s poor economy and state finances, Schwarzenegger and his chief rivals — Democratic Lt. Gov. Cruz Bustamante and Republican state Sen. Tom McClintock — are more focused on taxes and government spending.

Schwarzenegger also addressed some of those issues Tuesday with voters and later in a briefing with reporters.

Asked how local governments would stay afloat under his plan to reduce vehicle license fees, Schwarzenegger recommended letting cities and counties retain property tax revenues now usurped by the state.

More than half of those revenues, or about $6 billion a year, are now sent to school districts in place of state financing, said Steve Szalay, executive director of the California State Association of Counties.

Szalay applauded Schwarzenegger’s plan but said the resulting gap in school funding likely couldn’t be closed with program cuts alone. “If he wants to reel back the vehicle license fee, we think he needs to raise revenue in some other way,” Szalay said.

Schwarzenegger has not adopted a no-new-taxes pledge. But on Tuesday, he predicted lost revenue from a scaled-back car tax could be found by being more vigilant about eliminating government waste and fraud.

Borrowing an idea suggested by Republican Peter Ueberroth, who recently dropped out of the gubernatorial race, Schwarzenegger suggested a tax amnesty program, saying it might round up $1 billion.

He also said he would move to renegotiate expensive energy contracts locked in during a state power crisis two years ago.

And he wants to renegotiate gaming compacts with casino-operating Indian tribes in the hopes of getting tribes to share revenue with the state. He noted tribes pay Connecticut 25 percent of their revenues, and said such an arrangement could pay for “thousands of police officers, thousands of teachers.”

Finally, Schwarzenegger told reporters that his Republican rival, who trails him by several points in recent polls, should drop out of the race for the good of the party.

“I think McClintock should think about it seriously,” he said. “I think it will be tougher to win this race with having two Republicans in there.”

The California Senate’s top Republican, Sen. Jim Brulte, on Tuesday joined a growing list of influential Republicans endorsing Schwarzenegger and pressuring McClintock to step aside.

Brulte stopped short of explicitly asking McClintock to drop out of the race. But the Rancho Cucamonga legislator said he doubts McClintock can win and that his candidacy could grab votes from Schwarzenegger and help Democrats beat the recall or elect Bustamante.

“At this time, in this election, I believe for Tom the governorship is simply a bridge too far,” said Brulte, a powerful fund-raiser and leader in the state party.

Schwarzenegger, asked at the forum Tuesday about hurdles to small-business owners, turned the subject again to women. “I want to make sure we pay attention to women, make sure that they can also start businesses,” he said.

He spoke of his marriage to NBC newswoman Maria Shriver and of her challenges, even as a multimillionaire and a member of the Democratic Kennedy family, juggling a career and child rearing.

“I see my wife every day struggling,” he said.