House prosecutors who led Donald Trump’s impeachment maintained they proved their case on Sunday while railing against Senate Republicans for “trying to have it both ways” in acquitting the former president.

A day after Mr Trump won his second Senate impeachment trial in 13 months, bipartisan support appeared to be growing for an independent September 11-style commission to ensure such a horrific assault could never happen again.

The end of the quick trial hardly put to rest the debate about Mr Trump’s culpability for the January 6 insurrection as the political, legal and emotional fallout unfolded.

More investigations into the riot were already planned, with Senate hearings scheduled later this month in the Senate Rules Committee. Democratic House Speaker Nancy Pelosi also has asked a retired Army General Russel Honore to lead an immediate review of the Capitol’s security process.

Legislators from both parties signalled on Sunday that even more inquiries were likely.

“There should be a complete investigation about what happened,” said Louisiana senator Bill Cassidy, one of seven Republicans who voted to convict Mr Trump. “What was known, who knew it and when they knew, all that, because that builds the basis so this never happens again.”

Mr Cassidy said he was “attempting to hold President Trump accountable,” and added that as Americans hear all the facts, “more folks will move to where I was”. He was censured by his state’s party after the vote, which was 57-43 to convict but 10 votes short of the two-thirds required.

A close Trump ally, GOP senator Lindsey Graham of South Carolina, said he looked forward to campaigning with Mr Trump in the 2022 election, when Republicans hope to regain the congressional majority.

But Mr Graham acknowledged Mr Trump had some culpability for the siege at the Capitol that killed five people, including a police officer, and disrupted politicians’ certification of Democrat Joe Biden’s White House victory.

“His behaviour after the election was over the top,” Mr Graham said. “We need a 9/11 commission to find out what happened and make sure it never happens again.”

The Senate acquitted Mr Trump of a charge of “incitement of insurrection” after House prosecutors laid out a case that he was an “inciter in chief” who unleashed a mob by stoking a months-long campaign of spreading debunked conspiracy theories and false violent rhetoric that the 2020 election was stolen from him.

Mr Trump’s lawyers countered that the then president’s words were not intended to incite the violence and that impeachment was nothing but a “witch hunt” designed to prevent him from serving in office again.

The conviction tally was the most bipartisan in American history but left Mr Trump to declare victory and signal a political revival while a bitterly divided GOP bickered over its direction and his place in the party.

The Republicans who joined Mr Cassidy in voting to convict were senators Richard Burr of North Carolina, Susan Collins of Maine, Lisa Murkowski of Alaska, Mitt Romney of Utah, Ben Sasse of Nebraska and Pat Toomey of Pennsylvania.

“It’s frustrating, but the founders knew what they were doing and so we live with the system that we have,” Stacey Plaskett, a House prosecutor who represents the Virgin Islands, said of the verdict, describing it as “heart-breaking”.

She added: “But, listen, we didn’t need more witnesses. We needed more senators with spines.”

On Sunday, several House impeachment managers sharply criticised minority leader Mitch McConnell, who told Republican senators soon before the vote that he would acquit Mr Trump.

In a blistering speech after the vote, Mr McConnell said the president was “practically and morally responsible for provoking the events of that day” but that the Senate’s hands were tied to do anything about it because he was out of office. But the Senate, in an earlier vote, had deemed the trial constitutional.

“It was powerful to hear the 57 guilties and then it was puzzling to hear and see Mitch McConnell stand and say not guilty and then minutes later stand again and say he was guilty of everything,” said Democratic representative Madeleine Dean.

“History will remember that statement of speaking out of two sides of his mouth.”

Ms Dean backed the idea of an impartial investigative commission “not guided by politics but filled with people who would stand up to the courage of their conviction”.

An independent 9/11 style commission, which probably would require legislation to create, would elevate the investigation a step higher, offering a definitive government-backed accounting of events.