WASHINGTON — Congress will move to establish an independent commission to investigate the attack on the Capitol on Jan. 6, including facts “relating to the interference with the peaceful transfer of power,” Speaker Nancy Pelosi of California announced on Monday.

In a letter to her Democratic colleagues in the House, Ms. Pelosi also promised to move forward in coming weeks with emergency funding legislation “for the safety of members and the security of the Capitol” after consulting with retired Gen. Russel L. Honoré, whom she had asked to examine security on Capitol Hill.

“Security is the order of the day: the security of our country, the security of our Capitol, which is the temple of our democracy, and the security of our members,” Ms. Pelosi wrote in the letter, adding that it was clear both from General Honoré’s findings and “from the impeachment trial that we must get to the truth of how this happened.”

Calls have grown for a bipartisan, independent investigation into the law enforcement and administrative failures that led to the first breach of the Capitol complex in two centuries, particularly after the Senate acquitted former President Donald J. Trump in his impeachment trial on a charge of inciting the rioters. For some lawmakers, such a commission offers the last major opportunity to hold Mr. Trump accountable.

“There’s still more evidence that the American people need and deserve to hear,” Senator Chris Coons, Democrat of Delaware, said over the weekend on ABC’s “This Week,” adding that a commission would “make sure that we secure the Capitol going forward and that we lay bare the record of just how responsible” Mr. Trump was for the attack.

Establishing such a commission would most likely require legislation if it were modeled on the 9/11 Commission, which embarked on a 20-month investigation after President George W. Bush signed a law mandating the panel investigate what caused the Sept. 11 attacks and how to prevent a similar attack. The commission ultimately offered recommendations that led to the reshaping of congressional oversight and intelligence coordination.

Ms. Pelosi said the panel would be assigned to “investigate and report on the facts and causes relating to the Jan. 6, 2021, domestic terrorist attack upon the United States Capitol complex” as well as “the interference with the peaceful transfer of power.”

A group of House Republicans wrote to Ms. Pelosi on Monday complaining that she had tapped General Honoré without input from their party and demanded that she answer questions about what she knew and what directions she gave ahead of the Jan. 6 attack. Republicans have already objected to Ms. Pelosi’s decision to install magnetometers outside the House chamber in response to concern about some lawmakers bringing firearms onto the chamber floor.

“It is easy to understand why we and our Senate counterparts remain skeptical that any of his final recommendations will be independent and without influence from you,” wrote the Republicans, including Representative Rodney Davis of Illinois, the top Republican on the House Administration Committee, and Jim Jordan of Ohio, the top Republican on the House Judiciary Committee.

Shaken by the siege on Jan. 6, which left many traumatized after hiding for their lives in their offices and in the House chamber, lawmakers have also asked to use campaign funds to pay for additional security in their districts. An emergency funding bill would most likely help fund security for lawmakers in the districts as well as at the Capitol, which remains surrounded by fencing and patrolled by National Guard troops.