Former attorney general Jeff Sessions has announced that he will run for his old US Senate seat in Alabama and made clear his first priority is putting to rest tensions with Donald Trump.

In a video declaring his candidacy, Mr Sessions focuses not on his tenure or his vision, but rather his enduring support for the president.

"When I left President Trump's Cabinet, did I write a tell-all book? No. Did I go on CNN and attack the president? No. Have I said a cross word about President Trump? No," Mr Sessions says. "As everyone knows, President Trump and I have had our ups and downs. But here's the important part: the President is doing great work for America."

The former attorney general, an early supporter of Mr Trump's run for president, served as his first attorney general, but fell out of favour with the president when he recused himself from overseeing the Justice Department's Russia investigation.

Their relationship never recovered and culminated with Mr Trump unceremoniously firing him in November 2018.

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Mr Sessions' desire to mend relations with the president at the onset of his campaign shows how damaging it is for a Republican to have Mr Trump as an antagonist, especially in a Republican primary.

Texas senator John Cornyn said he warned Mr Sessions during a recent conversation about his potential candidacy that he needed to make up with the US president.

"He is a friend of mine. I'll be doing everything I can to encourage him," Mr Cornyn said. "The problem, as I pointed out to him, is, 'I think your life is going to be very difficult unless you work out some sort of reconciliation with the president.'"

Mr Trump has threatened to attack Mr Sessions if he enters the race, telling Senate Republican leaders that he did not want his ally-turned-foe to run in what already promises to be a contentious primary.

Mr Trump didn't mention Mr Sessions during a recent donor event for the Senate Leadership Fund, the main super political action committee (PAC) dedicated to electing Republicans to the Senate, according to a person in attendance.

The seat, which Mr Sessions easily held for two decades before leaving for the Trump administration, is currently filled by a Democrat.

Doug Jones won the seat from a traditionally conservative state in a special election in 2017, beating Republican Roy Moore, who faced allegations that he propositioned teenagers when he was in his 30s.

Mr Moore is running again, joined by congressman Bradley Byrne and several other Republicans in the state.

President Trump told reporters he is 'disappointed' with Attorney General Jeff Sessions

Asked about Mr Sessions' candidacy during an interview on SiriusXM's The Joe Madison Show, Mr Jones said: "Before he challenges me, he's got about six challengers in that Republican primary that are already sniping at him. . . . It's going to be a really divisive primary," . "And now you've got somebody else jumping in there that the president of the United States has said it was the biggest mistake he's ever made by appointing him."

Senate majority leader Mitch McConnell, has shared concerns that Mr Sessions' running could create a messy primary contest for a seat that Republicans say they have to win back, according to people familiar with the matter who spoke on the condition of anonymity to discuss the issue.

Mr Trump has repeatedly denigrated Mr Sessions to allies and White House aides in recent days, people familiar with his comments said.

Senator Lindsey Graham, one of Mr Trump's closest allies on Capitol Hill, called Mr Sessions a "fine man" but added that he wouldn't endorse him in the primary.

"The whole campaign's going to be around what President Trump said about Jeff Sessions," Mr Graham said. "I think Jeff knows what he's getting into and we'll leave it up to the voters of Alabama."

Jeff Sessions speaks in a campaign video posted to social media (@jeffsessions)

Mr Sessions appeared on Tucker Carlson's show on Fox News after releasing his campaign video and said he hoped to have Mr Trump's support.

Mr Sessions said he understood how "painful" the Russia investigation was for the president and that Mr Trump saw Mr Sessions' recusal as a "pivotal moment."

Mr Sessions accused current Republican senators of not doing enough to advance Mr Trump's agenda.

"I think some of them are still standoffish, some of them almost give the impression that maybe he'll just fail or it won't happen and we won't have to deal with it," Mr Sessions told Mr Carlson.

Robert De Niro appears as Robert Muller in Saturday Night Live Jeff Sessions farewell sketch

Ahead of his formal announcement, Republican senators offered tepid support for their former colleague's attempt at a comeback.

Many GOP senators demurred when asked about his possible run, saying they didn't involve themselves in other races' primary contests – even for someone who served with them for years.

Others voiced praise of Mr Sessions' previous work as a senator but also trepidation about his acrimonious relationship with Mr Trump.

Behind the scenes, senator Richard Shelby, has been working to secure endorsements from Senate Republicans, according to two senators who spoke on the condition of anonymity to describe private conversations, and has told other Republicans privately for weeks that if Mr Sessions chooses to run, he would support him and aid him.

Senator Roy Blunt, was among the few who openly stated their support for a Sessions run. Asked whether Mr Trump's attacks on Mr Sessions would hurt him given the president's popularity in the state, Mr Blunt said Mr Sessions had "been pretty popular in Alabama himself".

Others shied away from backing Mr Sessions, instead saying they'd wait until after the primary to throw their support behind a candidate.

"I believe generally in primaries haven't gotten involved. Not even in my state. I'd have to look at it if he ultimately makes a decision," Senator Thom Tillis, said. "The only thing I will say about Alabama is that I am an anyone-but-Moore supporter."

Senator Kevin Cramer, had a similar lukewarm reaction.

"I have all I can do to keep track of me. He should do whatever he wants to do," Mr Cramer said. "He's free to run if he wants to run."

When asked whether Mr Trump's scorn would hurt Mr Sessions' chances, Mr Cramer said, "Well, I guess I'd rather go into a Republican primary with the president's support than without it, but Jeff Sessions is iconic and you know obviously a player right out of the chute. But I don't know."

Asked what Mr Sessions could do to win back Mr Trump's support, Mr Cramer replied, "Win."