WASHINGTON (AP) — Sen. John McCain swept a string of delegate-rich, East Coast primaries Tuesday night, reaching for command of the race for the Republican presidential nomination. Democrats Hillary Rodham Clinton and Barack Obama traded victories in an epic struggle from Connecticut to California.

The former first lady said, ‘‘I look forward to continuing our campaign and our debate about how to leave this country better off for the next generation.’’

McCain, the early Republican front-runner whose campaign nearly unraveled six months ago, won in New York, New Jersey, Connecticut and Delaware to gain all 198 delegates at stake there. He also put Illinois and Oklahoma in his column.

Former Arkansas Gov. Mike Huckabee won a series of Bible Belt victories, in Alabama and Georgia as well as his own home state. He also triumphed at the Republican West Virginia convention, and told The Associated Press in an interview he would campaign on. ‘‘The one way you can’t win a race is to quit it, and until somebody beats me, I’m going to answer the bell for every round of this fight,’’ he said.

Romney, the former governor of Massachusetts, won a home state victory. He also took Utah, where fellow Mormons supported his candidacy. He, too, breathed defiance. ‘‘We’re going to go all the way to the convention. We’re going to win this thing,’’ he told supporters in Boston.

Democrats played out a historic struggle between Clinton, seeking to become the first female president and Obama, hoping to become the first black to win the White House.

Clinton won at home in New York as well as in Massachusetts, New Jersey, Missouri, Oklahoma, Tennessee and Arkansas, where she was first lady for more than a decade. She also won the caucuses in American Samoa.

Obama won Connecticut, Georgia, Alabama, Delaware, Utah and his home state of Illinois. He also prevailed in North Dakota, Minnesota and Kansas, three caucus states.

After an early series of low-delegate, single-state contests, Super Tuesday was anything but small — its primaries and caucuses were spread across nearly half the country in the most wide-open presidential campaign in memory.

The result was a double-barreled set of races, Obama and Clinton fighting for delegates as well as bragging rights in individual states, the Republicans doing the same.

Polling place interviews with voters suggested subtle shifts in the political landscape, potentially significant as the races push on through the campaign calendar.

For the first time this year, McCain ran first in a few states among self-identified Republicans. As usual, he was running strongly among independents. Romney was getting the votes of about four in 10 people who described themselves as conservative. McCain was wining about one-third of that group, and Huckabee about one in five.

Overall, Clinton was winning only a slight edge among women and white voters, groups that she had won handily in earlier contests, according to preliminary results from interviews with voters in 16 states leaving polling places. Obama was collecting the overwhelming majority of votes cast by blacks.

Clinton was gaining the votes of roughly six in 10 Hispanics, and she hoped the edge would serve her well as the race turned west to Arizona, New Mexico and California, the biggest prize with 370 delegates.

The allocation of delegates lagged the vote count by hours. That was particularly true for the Democrats, who divided theirs roughly in proportion to the popular vote.

Nine of the Republican contests were winner take all, and that was where McCain piled up his lead.

The Arizona senator had 345 delegates to 129 for Romney and 115 for Huckabee. It takes 1,191 to clinch the presidential nomination at next summer’s convention in St. Paul, Minn.

Overall, Clinton had 348 delegates to 282 for Obama, out of the 2,025 needed to secure victory at the party convention in Denver. Clinton’s advantage is due to her lead among so-called superdelegates, members of Congress and other party leaders who are not selected in primaries and caucuses — and who are also free to change their minds.

Alabama and Georgia gave Obama three straight Southern triumphs. Like last month’s win in South Carolina, they were powered by black votes.

Democrats and Republicans alike said the economy was their most important issue. Democrats said the war in Iraq ranked second and health care third. Republican primary voters said immigration was second most important after the economy, followed by the war in Iraq.

The survey was conducted in 16 states by Edison Media Research and Mitofsky International for The Associated Press and television networks.

McCain was the Republican front-runner, all but unchallenged in winner-take-all primaries in New York, New Jersey and Connecticut. He looked for a home-state win in Arizona, as well.

Democrats Obama and Clinton conceded in advance that neither was likely to emerge from the busiest day in primary history with anything more than a relatively narrow edge in convention delegates.

‘‘Senator Clinton, I think, has to be the prohibitive favorite going in given her name recognition, but we’ve been steadily chipping away,’’ said Obama, seeking to downplay expectations.

As she voted in Chappaqua, N.Y., the former first lady said, ‘‘The stakes are huge.’’

Already, both campaigns were looking ahead to Feb. 9 contests in Louisiana, Nebraska and Washington state and Feb. 12 primaries in Maryland, Virginia and the District of Columbia. And increasingly, it looked like the Democrats’ historic race between a woman and a black man would go into early spring, possibly longer.

The de facto national primary was the culmination of a relentless campaign that moved into overdrive during Christmas week.

After a brief rest for the holiday, the candidates flew back to Iowa on Dec. 26 for a final stretch of campaigning before the state’s caucuses offered the first test of the election year. New Hampshire’s traditional first-in-the-nation primary followed a few days later, then a seemingly endless series of campaign days interspersed by debates and a handful of primaries and caucuses.

Along the way, the poorest performers dropped out: Democratic Sens. Joe Biden and Chris Dodd, New Mexico Gov. Bill Richardson and Rep. Dennis Kucinich of Ohio; and Republican Reps. Duncan Hunter and Tom Tancredo, and former Tennessee Sen. Fred Thompson.

Former Sen. John Edwards pulled out of the Democratic race last week, and former New York Mayor Rudy Giuliani left the Republican field.

Edwards offered no endorsement as he exited, instead leaving Obama and Clinton to vie for help from his fundraisers and supporters.

But Obama benefited from an endorsement by Sen. Edward M. Kennedy, who made a series of campaign appearances in California as well as his home state of Massachusetts.

Giuliani quit the race and backed McCain in the same breath, clearing the way for the Westerner in New York and New Jersey.

Giuliani’s departure also made it possible for California Gov. Arnold Schwarzenegger to back McCain. Schwarzenegger said he would not have done so as long as the former mayor was in the race.

Obama and Clinton spent an estimated $20 million combined to advertise on television in the Feb 5 states.

Obama spent $11 million, running ads in 18 of the 22 states with Democratic contests. Clinton ran ads in 17, for a total of $9 million.

Neither advertised in Illinois, Obama’s home state.