WASHINGTON — Donald Trump won seven of 11 states on Super Tuesday, a string of victories that puts the maverick billionaire close to the brink of claiming the Republican presidential nomination.

"I feel awfully good," Trump told reporters in Florida after being asked if he believes he is the presumptive GOP nominee.

Ted Cruz, who took Oklahoma, Alaska and his home state of Texas on Tuesday, called on other rivals to drop out and present a united front against the the New York billionaire.

Marco Rubio — who won the Minnesota caucuses, his first victory in the campaign — vowed a long fight to deny the current front-runner the delegates needed to actually win the nomination at the July convention in Cleveland.

Speaking to supporters in Palm Beach, Fla., Trump called it "an amazing evening," and predicted he would win the March 15 primary in Rubio's home state of Florida, and the fall election over Democrat Hillary Clinton.  

"Once we get all of this finished," Trump said, "I am going to go after one person and that’s Hillary Clinton."

Trump took Georgia, Alabama, Tennessee, Massachusetts, Arkansas, Virginia, and Vermont, while the Alaska caucuses remained too close to call.

The wins figure to give Trump a large lead in convention delegates. The billionaire's status as an "outsider" who has never held public office helped in most of these contests, according to exit polls. GOP voters expressed dislike for the current Republican Party establishment. 

John Kasich ran a close second to Trump in Vermont. 

New Jersey Gov. Chris Christie, who endorsed Trump last week, introduced the front-runner at his Palm Beach event, declaring him "the clear winner of Super Tuesday," said said his victories are "the beginning of Donald Trump bringing the Republican Party together" for victory in the fall.

While congratulating Cruz on his wins in Texas and Oklahoma, Trump branded Rubio as "the big loser of the night." 

Cruz, meanwhile, trumpeted his wins in Texas and Oklahoma, and said the race enters a "new phase" that pits him against Trump, whom he also defeated in Iowa last month. Speaking before the call of Rubio's win in Minnesota, Cruz told backers that, after Tuesday's results, he has "the only campaign that has beaten, that can beat, and that will beat Donald Trump."

Rubio vowed to fight on, saying he expects to pick up many many delegates Tuesday and to sweep to victory in Florida in two weeks, establishing himself as the main alternative to Trump.

"Two weeks from tonight, right here in Florida, we are going to send a message loud and clear," Rubio told backers in Miami. "That the party of Lincoln and Reagan, and the presidency of the United States, will never be held by a con artist."

As returns came in Tuesday, the Rubio campaign sent an e-mail to supporters vowing a "long war" against Trump, saying that "we are NOT going to hand over our party to a dangerous con artist."

Kasich, the governor of Ohio, also hopes to be the last candidate standing between Trump and the nomination, figuring that establishment forces will then rally around him. While Kasich had little to cheer about Tuesday, he is looking ahead to more favorable primaries in his neighboring state of Michigan (next Tuesday) and his home state of Ohio (March 15).

Citing respectable finishes Tuesday in Vermont, Massachusetts, and Virginia, Kasich told supporters that "we have absolutely exceeded expectations."

Trump's Tuesday wins added to his victories in New Hampshire, South Carolina and Nevada, following a second'place finish in the opening contest in Iowa.

There were 595 GOP delegates available Tuesday — nearly half the number necessary to claim the Republican presidential nomination.

Rubio supporters echoed their candidate's optimism as they prepared for his "kickoff rally" in Miami. “The most important thing is winning delegates tonight, not states,” said Gemma Arencibia, 61, a retired school director from Sunny Isles Beach, Fla.

Kasich echoed those sentiments on behalf of his campaign, telling supporters in Virginia: “When this election moves north, fasten your seat belts ... When I win Ohio, it will be a whole new day I can promise you that.”

Trump still faces fierce opposition from many Republicans. On Tuesday, House Speaker Paul Ryan, R-Wisc., implicitly criticized the businessman for declining to repudiate the endorsement of the Ku Klux Klan during a television interview broadcast Sunday.

In his Super Tuesday news conference, Trump said he expects to have a great relationship with Republican congressional leaders, including Ryan — "and if I don’t, he’s going to have to pay a big price, OK?"

Ben Carson, who remains in the race but made no strong showings Tuesday, told MSNBC's Morning Joe that people have asked him to exit the race, but his supporters have begged him to stay.

“They're continuing to support us tremendously economically,” Carson said.

Carson also called for a private meeting of all five Republican candidates before Thursday's scheduled debate in Detroit, saying he is "concerned with the lack of civility currently being displayed in the race."

Contributing: Jennifer Jacobs, Deirdre Shesgreen, Alan Gomez, Chrissie Thompson