Schwarzenegger put his star power to work for the president, praising him for "perseverance, character and leadership" in a time of war and terror.
Neither speaker mentioned John Kerry, a sharp change from the first night of the convention, when Mr. Bush's rival was harshly criticized by former New York Mayor Rudy Giuliani.
Republican convention planners scripted an evening that reintroduced the theme of compassionate conservatism that Mr. Bush ran on successfully four years ago.
The Austrian-born California governor drew on his own immigrant story to cast the GOP as a party of opportunity. "I want other people to get the same chances I did, the same opportunities," he said.
"And I believe they can. That's why I believe in this country, that's why I believe in this party and what's why I believe in this president," Schwarzenegger said in a prime-time speech to Republican delegates.
Schwarzenegger and the first lady had their turns at the podium as 2,508 delegates formally bestowed their nomination on the president for a second term in office.
Mr. Bush introduced his wife by satellite from a campaign stop in Pennsylvania.
"I'm a lucky man to have Laura at my side, and America will be lucky to have her in the White House four more years," he said.
The Bushes' 22-year-old twin daughters, Jenna and Barbara, addressed the delegates in Madison Square Garden just ahead of their father's live shot.
Republicans met inside their heavily fortified convention hall as police arrested more than 1,000 anti-GOP demonstrators in the surrounding streets on a day heavy with protests. By evening, authorities wrapped an entire midtown Manhattan block in orange netting, working to contain demonstrators who vowed to march on the Garden itself.
Mr. Bush, locked in a tight re-election race, campaigned across three battleground states and worked to extinguish a convention-week controversy of his own making. "In this different kind of war, we may never sit down at a peace table. But make no mistake about it, we are winning, and we will win" the war on terror, he told an American Legion convention in Tennessee, one day after saying he didn't think victory would be possible.
Mr. Bush's Democratic challenger, Sen. John Kerry, spent the day at home in Nantucket, Mass., as his campaign settled on plans to place $45 million in television advertising in 20 battleground states through Election Day. The commercials will run on broadcast stations and cable, and include appeals to minority voters whom Democrats need to turn out in large numbers on Nov. 2 if they are to deny Mr. Bush a second term.
Mr. Bush arrives in New York on Wednesday, a day ahead of his nomination acceptance speech. Vice President Dick Cheney was to speak Wednesday night at the convention along with keynote speaker Zell Miller, a Democratic senator from Georgia. While Democrats are peeved at Miller for his speaking role, they plan to focus most of their criticism on Cheney.
The Democrats' rapid-response team planned to target Cheney on Wednesday during their briefing at the war room near the Republican convention.
"When Dick Cheney takes the stage at the convention, we will be reminding Americans about Dick Cheney's record, not only his abysmal failure as vice president but the sweetheart deals that his administration has cut with the company that he used to lead," said Matt Bennett, a spokesman for the Democrats. Halliburton, the company that was headed by Cheney before he became Mr. Bush's running mate, has a multibillion-dollar contract for work done in Iraq.
On Wednesday, Cheney's wife, Lynne Cheney, defended the vice president's role in the administration, saying he's an asset to Mr. Bush.
"I think Dick has, you know, brought just a world of expertise to this job, which he really didn't plan on having, but has enjoyed greatly," Cheney's wife, Lynne Cheney told CBS' Early Show co-anchor Harry Smith. "I think the president values his advice, and, in the end, I suspect that's the most important audience."
In her convention remarks, Mrs. Bush said that her husband's leadership has helped 50 million men, women and children win freedom over the past four years, a reference to wars in Afghanistan and Iraq.
"I want to talk about the issue that I believe is most important for my own daughters, for all our families, and for our future: George's work to protect our country and defeat terror so that all children can grow up in a more peaceful world," she added.
Schwarzenegger, in a speech brimming with optimism, said, "America is back! Back from the attack on our homeland, back from the attack on our economy, back from that attack on our way of life. We're back because of the perseverance, character and leadership " of George W. Bush.
Schwarzenegger urged optimism about the country's economy, too.
"To those critics who are so pessimistic about our economy, I say: 'Don't be economic girlie men!'" Schwarzenegger said — a line from a Saturday Night Live spoof of him that he used against Democratic legislators earlier this year.
Schwarzenegger never mentioned Kerry, with whom he is friendly, but he did get in some digs at the Democrats. "One of my movies was called 'True Lies,'" he said. "It's what the Democrats should have called their convention."
Schwarzenegger was the latest moderate Republican to take a prominent role at a convention nominating a far more conservative president. The governor and the president disagree on issues including abortion rights, which Schwarzenegger supports, and amending the Constitution to ban gay marriage, which he opposes.
A parade of speakers walked onto a podium that bore the words "People of Compassion" as a backdrop. They praised the president's efforts to battle AIDS, combat breast cancer, promote adoption and enact far-reaching educational reforms.