WASHINGTON — One day after former president Donald Trump won his second Senate impeachment trial in two years, bipartisan support appeared to be growing for an independent Sept. 11-style commission to investigate the Jan. 6 riot at the U.S. Capitol to make sure that such an assault could never happen again.

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

More investigations into the riot already are planned, with Senate hearings scheduled later this month in the Senate Rules Committee.

House Speaker Nancy Pelosi (D., Calif.) has asked retired Army Lt. Gen. Russel Honore to lead an immediate review of the Capitol’s security process.

Lawmakers from both parties signaled Sunday that more inquiries are likely.

“There should be a complete investigation about what happened,” said Sen. Bill Cassidy (R., La.), one of seven Republicans who voted to convict 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 Republican Party after the vote, which was 57-43 to convict but 10 votes short of the two-thirds required.

Sen. Lindsey Graham (R., S.C.), a Trump ally, 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 that the former president had some culpability for the attack at the Capitol that killed five people, including a police officer, and disrupted lawmakers’ certification of Democrat Joe Biden’s White House victory.

“His behavior 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 the “inciter in chief” who unleashed a mob by stoking a months-long campaign of spreading conspiracy theories and allegations that the 2020 election was stolen from him.

Mr. Trump’s lawyers countered that Mr. Trump’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.

The Republicans who joined Mr. Cassidy in voting to convict were Sens. 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.

Mr. Graham spoke with Mr. Trump Saturday night and acknowledged that the former president is “mad at some folks,” but also “ready to move on and rebuild the Republican Party” and “excited about 2022.”

In their conversations, Mr. Graham said he told Mr. Trump, who has threatened to start his own party to punish disloyal Republicans, that the GOP needs him to win.

“I said, ‘Mr. President, this MAGA movement needs to continue. We need to unite the party. Trump-plus is the way back in 2022,’” Mr. Graham told Fox News Sunday.

“My goal is to win in 2022 to stop the most radical agenda I’ve seen coming out of the Democratic presidency of Joe Biden. We can’t do that without Donald Trump, so he’s ready to hit the trail and I’m ready to work with him,” Mr. Graham said.

Several House impeachment managers on Sunday criticized Senate Minority Leader Mitch McConnell (R., Ky.), who told Republican senators shortly before the vote that he would vote to acquit Mr. Trump.

After the vote, Mr. McConnell said the former 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 Mr. Trump 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 Rep. Madeleine Dean (D., Pa.).

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

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.

Ms. Pelosi has expressed support for such a commission while emphasizing that the members who sit on it would be key.

Such a panel could pose risks of sharpening partisan divisions or overshadowing President Biden’s legislative agenda.

“There’s still more evidence that the American people need and deserve to hear and a 9/​11 commission is a way to make sure that we secure the Capitol going forward,” said Sen. Chris Coons (D., Del.), a Biden ally.