Federal prosecutors recommended on Thursday that two top leaders of the far-right Proud Boys convicted of seditious conspiracy in the Jan. 6 attack on the Capitol be sentenced to 33 years in prison, the stiffest penalties requested so far out of more than 1,000 people charged in the sprawling investigation.

In seeking to severely punish the two Proud Boys, Enrique Tarrio, the former chairman of the group, and Joseph Biggs, one of Mr. Tarrio’s top lieutenants, prosecutors asked the judge in the case to increase their sentences with what is known as a terrorism enhancement.

“The defendants understood the stakes, and they embraced their role in bringing about a ‘revolution,’” the prosecutors wrote in a 155-page filing to Judge Timothy J. Kelly of the U.S. District Court in Washington. “They unleashed a force on the Capitol that was calculated to exert their political will on elected officials by force and to undo the results of a democratic election.”

“The foot soldiers of the right aimed to keep their leader in power,” the prosecutors continued, referring to former President Donald J. Trump. “They failed. They are not heroes; they are criminals.”

In their request to Judge Kelly, the prosecutors also asked for tough sentences for the other three defendants in the case: Zachary Rehl, Ethan Nordean and Dominic Pezzola.

Prosecutors asked that Mr. Rehl, the former president of the Proud Boys chapter in Philadelphia, be sentenced to 30 years in prison; that Mr. Nordean, who ran a Proud Boys chapter in Seattle, serve 27 years; and that Mr. Pezzola, a new recruit to the group from Rochester, N.Y., face 20 years behind bars.

All of the men, except for Mr. Pezzola, were found guilty in May of seditious conspiracy, a rarely used criminal charge that harks back to the Union’s efforts to protect the federal government against secessionist rebels during the Civil War. To prove sedition, prosecutors have to persuade a jury that defendants used force to oppose the authority of the federal government or the execution of federal law.

Until the government’s filing late on Thursday night, the longest sentence prosecutors had asked for in a Jan. 6-related case was the 25-year term requested for Stewart Rhodes, the founder and leader of another far-right group, the Oath Keepers militia.

Mr. Rhodes was ultimately sentenced to 18 years in prison. The five Proud Boys defendants are scheduled to be sentenced in the same courthouse at the end of August.

Norm Pattis, a lawyer for both Mr. Biggs and Mr. Rehl, took issue with the government’s attempt to impose the terrorism enhancement in court papers filed a few hours before the government made its recommendations to Judge Kelly.

“The defendants are not terrorists,” Mr. Pattis wrote. “Whatever excesses of zeal they demonstrated on Jan. 6, 2021, and no matter how grave the potential interference with the orderly transfer of power due to the events of that day, a decade or more behind bars is an excessive punishment.”

But prosecutors said in their filing to Judge Kelly that the five men had “led the attack on the Capitol” and contributed to “four pivotal breach points” at the building “in the first 80 minutes of the riot.”

“No other group of defendants had a bigger impact on the events of Jan. 6 than these defendants and the men in their command,” the prosecutors wrote.