WASHINGTON (Reuters) - U.S. Republican Senator Orrin Hatch said on Tuesday he will not seek re-election in November, opening the door to a potential Senate bid by Mitt Romney, the 2012 Republican presidential candidate and one of the party’s harshest critics of President Donald Trump.

“Every good fighter knows when to hang up the gloves. And for me, that time is soon approaching,” Hatch said in a video statement posted on Twitter. “That’s why after much prayer and discussion with family and friends, I’ve decided to retire at the end of this term.”

Hatch, 83, of Utah, is the most senior Republican in the U.S. Senate, having first been elected in 1976. He is chairman of the tax-writing Senate Finance Committee. Trump has credited him with helping shepherd a massive tax overhaul through Congress last month.

Hatch steps down amid speculation that Romney, the former Massachusetts governor who ran against Democratic President Barack Obama in 2012, would run for his Senate seat. Romney, who is a Mormon, has close ties to Utah, a state with a majority-Mormon population.

In a statement on Twitter, Romney praised Hatch for his service but he did not say if he would enter the Senate race.

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A close Romney adviser, speaking on condition of anonymity, said Hatch’s decision increased the odds that Romney would consider jumping in, saying that Romney would likely decide relatively soon whether to seek the Senate seat in the Republican-leaning state.

If he does decide to mount a campaign, Romney, who gained national prominence as head of the 2002 Salt Lake City Olympics, would be the front-runner, said Republican strategist Joe Brettell.

“Romney’s name ID, fund-raising network and business acumen will immediately vault him to the top of the Senate GOP list,” Brettell said. “The question is whether he can happily weather a body currently known more for partisan rancor than the Mr. Fixit role he’s played all his life.”

In a tweet, Trump congratulated Hatch on “an absolutely incredible career.” Trump called Hatch a “tremendous supporter” and said he will be “greatly missed” in the Senate.

Trump said last month he wanted Hatch to run for another six-year Senate term in 2018, in a slap at Romney, who was one of Trump’s harshest Republican critics during the 2016 presidential campaign.