WASHINGTON, June 26 (Xinhua) -- The so-called "Trump effect" prevailed as seven U.S. states held primaries or runoffs on Tuesday, with at least three Republican candidates projected as winners thanks to President Donald Trump's endorsement.

"A big night!" Trump tweeted Tuesday night.

South Carolina Governor Henry McMaster, an early ally of Trump during the 2016 campaign, fended off a first-time challenger in a primary runoff after the president campaigned with him at his election eve rally in the southern U.S. state.

McMaster's rival had tried to argue he was the most Trump-like candidate as an outsider businessman.

"They will say, 'Donald Trump suffered a major, major defeat in the great state of South Carolina. It was a humiliating defeat for Donald Trump.' So please get your asses out tomorrow and vote," Trump told McMaster's rally Monday night.

"Congratulations to Governor Henry McMaster on your BIG election win!!" the president tweeted Tuesday night.

Trump then offered congratulations to New York Representative Dan Donovan, who won the Republican primary in a district where Trump won by about 10 points in 2016. Trump endorsed Donovan via Twitter last month, warning that Donovan's challenger, who also had tried to campaign as the more pro-Trump candidate, would be unelectable.

"Tremendous win for Congressman Dan Donovan. You showed great courage in a tough race! New York, and my many friends on Staten Island, have elected someone they have always been very proud of. Congratulations!" Trump tweeted.

In the latest news for Trump-backed candidates, Mitt Romney, the former Massachusetts governor and 2012 Republican presidential candidate, was also projected to win the Utah Senate primary runoff on late Tuesday night.

Romney once publicly criticized Trump during the 2016 presidential campaign, calling him "a phony, a fraud." "He (Trump) gets a free ride to the White House, and all we get is a lousy hat."

Romney has heavily muted his negative comments following Trump's election victory. But he was often criticized by Trump supporters and even called a "Republican in name only."

Despite their bumpy relationship, Trump endorsed Romney earlier this year, tweeting that Romney would "make a great Senator."

"Big and conclusive win by Mitt Romney. Congratulations! I look forward to working together -- there is so much good to do," Trump tweeted late Tuesday night.

Trump endorsements obviously boost incumbents, local analysts said.

Compared with recent midterms, more American voters say their view of the president, positive or negative, will influence their vote for the Congress, according to a new poll by Pew Research Center released last week.

As high as 60 percent of U.S. voters say they consider their midterm vote as essentially a vote either for Donald Trump or against him, the poll found.