Donald Trump’s acquittal in his second Senate impeachment trial has triggered friction and recrimination within the Republican party between lawmakers who want to break from the former president and those who still embrace his brand of politics.

Trump was exonerated on Saturday even after seven Republican senators voted to convict him of inciting an insurrection that led to last month’s deadly assault on the US Capitol. Under the US constitution, two-thirds of the Senate was needed to find him guilty in order for him to be convicted.

But the final 57-43 vote has revealed serious tensions within the Republican party over how to recover from their recent election losses.

After voting to acquit Trump, Mitch McConnell, the Republican Senate leader, excoriated the former president, describing his actions in the run-up to the January 6 riot as “a disgraceful dereliction of duty”.

“There is no question that President Trump is practically and morally responsible for provoking the events of that day,” he said.

On Sunday, Lindsey Graham, the South Carolina senator and fierce Trump ally, sharply criticised McConnell, saying his words would be used against Republican candidates in next year’s midterm elections, when the GOP tries to win back control of Congress.

“I think Senator McConnell’s speech, he got a load off a chest obviously but unfortunately he put a load on the back of Republicans,” he told Fox News Sunday.

“Trump plus is the way back in 2022.”

Graham also suggested that Lara Trump, the ex-president’s daughter-in-law, should run for a senate seat in North Carolina, which is due to become vacant in 2022. “I think she represents the future of the Republican Party,” he said.

Some moderate Republicans have sought distance themselves from the former president. Larry Hogan, governor of Maryland and a potential 2024 presidential candidate, said the party needed to abandon Trump’s politics if it was going to remain competitive across the country.

“There was a hostile takeover of the Republican party”, he told NBC News. “I think we've got to move on from the cult of Donald Trump and return to the basic principles that the party has always stood for.”

Trump, who has kept a low profile since snubbing Joe Biden’s inauguration last month, seemed to make his own intentions clear in a statement on Saturday: “Our historic, patriotic and beautiful movement to Make America Great Again has only just begun.”

“In the months ahead I have much to share with you, and I look forward to continuing our incredible journey together to achieve American greatness for all of our people,” he added.

The former president, 74, has not ruled out running for president again in 2024. But he is facing several criminal probes, including investigations in Georgia and New York, that could complicate his political ambitions.

There were signs of a backlash against the seven Republicans — Richard Burr of North Carolina, Bill Cassidy of Louisiana, Maine’s Susan Collins, Alaska’s Lisa Murkowski, Mitt Romney of Utah, Ben Sasse of Nebraska and Pennsylvania’s Pat Toomey — who voted with Democrats to convict the president.

Cassidy defended his decision on Sunday after Trump-loyal Republican officials in Louisiana said he was “part of the problem” and should not expect a “warm welcome” when he returns to his home state.

“As these facts become more and more out there, if you will, and folks have a chance to look for themselves, more folks will move to where I was,” Cassidy told ABC News. “People . . . want to trust their leaders. They want people to be held accountable.”

Lawrence Tabas, chair of the Pennsylvania Republican party, issued a sharply worded statement on Saturday condemning Toomey for his vote to convict Trump.

"I share the disappointment of many of our grassroots leaders and volunteers over Senator Toomey's vote today, " he said.

Several Republican lawmakers have either publicly or privately condemned Trump’s behaviour on January 6. But few have been willing to make a clean break with the former president, given the grip he still holds over large swaths of the Republican base.

At the same time, McConnell and others are grappling with whether the party can win back moderate Republicans and independents who abandoned the GOP over Trump last November, and public opinion polls show are outraged by January 6.

Murkowski, who will be up for re-election in 2022, dismissed suggestions that she would lose her seat over the impeachment vote. “If I can't say what I believe that our president should stand for, then why should I ask Alaskans to stand with me?”