WASHINGTON — Mitt Romney laid claim to the fiercely contested Republican presidential nomination Tuesday night with a fistful of primary triumphs, then urged all who struggle in a shaky U.S. economy to “hold on a little longer, a better America begins tonight.”

Eager to turn the political page to the general election, Romney accused President Obama of “false promises and weak leadership.” He said, “Everywhere I go, Americans are tired of being tired, and many of those who are fortunate enough to have a job are working harder for less.”

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GOP presidential candidate Mitt Romney and his wife, Ann, wave to supporters Tuesday in Manchester, N.H. Romney won primaries in five Northeastern states Tuesday. The Associated Press

The former Massachusetts governor spoke as he swept primaries in Connecticut, Rhode Island, Delaware, Pennsylvania and New York, the first since former Sen. Rick Santorum, R-Pa., conceded the nomination.

“Mitt Romney is going to be the nominee, and I’m going to support the nominee,” Santorum said on CNN. He added he intended to meet today with the winner’s aides.

Romney, speaking to cheering supporters, in New Hampshire, said, “The last few years have been the best Barack Obama can do, but it’s not the best America can do.”

He delivered his remarks to a national TV audience as well from the state where he won his first primary of the campaign and one of about a dozen states expected to be battlegrounds in the summer and fall campaign for the White House.

Obama campaigned during the day in two others — North Carolina and Colorado — making the case that, however slowly, the economy is growing stronger.

“Our businesses have added more than 4 million jobs over the past two years, but we all know there’s still too many Americans out there looking for work or trying to find a job that pays enough to cover the bills and make the mortgage,” the president said.

“We still have too many folks in the middle class that are searching for that security that started slipping away years before the recession hit.”

Six months before the election, opinion polls show the economy to be the top issue by far in the race. The same surveys point toward a close contest, with several suggesting a modest advantage for the incumbent.

Obama won the presidency in 2008 in the midst of the worst recession since the Great Depression, and since then economic growth has rebounded slowly and joblessness has receded gradually, although housing prices continue to drop in many areas of the country.

In a sign that Romney was treating the moment Tuesday night as something of an opening of the general election campaign, his speech seemed aimed at the millions of voters who have yet to pay close attention to the race for the White House.

He blended biographical details, an attack on Obama and the promise of a better future, leaving behind his struggle to engage conservative voters.

“As I look around at the millions of Americans without work, the graduates who can’t get a job, the soldiers who return home to an unemployment line, it breaks my heart,” he said. “This does not have to be. It is the result of failed leadership and of a faulty vision.”

Obama, unchallenged for the Democratic nomination, has a head start in campaign organizing and fundraising.

Already, he and aides are working to depict Romney and Republicans as pursuing new tax breaks for the wealthy while seeking to cut programs that benefit millions of victims of the recession as well as other lower-income Americans.

The president campaigned on two college campuses during the day, pitching his proposal to prevent a scheduled hike in interest on new student loans.

Romney, freed of serious primary competition, announced his own general support for the proposal, even though it appears a GOP-drafted budget in the House envisioned no effort to change the pending increase.

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