The pair had to be separated by a Capitol staffer, reporters wrote on Twitter.
Lawmakers remained on Capitol Hill well after midnight after a long Wednesday that included pro-Trump demonstrators storming the Capitol, forcing members of Congress to barricade themselves for safety until the building could be secured.
They resumed debating the electoral college results around 8 p.m. ET and the near-fisticuffs sparked around 2 a.m. ET Thursday, Fox News' Chad Pergram wrote on Twitter.
Several reporters said the dispute may have been sparked by Pennsylvania Democratic Rep. Conor Lamb's description of the Wednesday rioting.
"It didn't materialize out of nowhere," Lamb said of the unrest, according to Mediaite.com. "It was inspired by lies. The same lies that you're hearing in this room tonight."
Lamb later shouted, "The truth hurts!" when some Republicans objected to his description of them as being liars.
As Lamb is speaking, a commotion is heard behind him, according to a C-SPAN video.
The potential brawl between the lawmakers would have pitted Harris, a 63-year-old U.S. Navy veteran who served in Operation Desert Storm, against Allred, a 37-year-old former college football player at Baylor who later spent some time with the NFL’s Tennessee Titans.
Harris, born in New York City, has represented Maryland’s 1st Congressional District since January 2011, while Allred, a native of Dallas, has represented the 32nd Congressional District in Texas since January 2019 and was reelected to a second term in November.
Fox News’ Chad Pergram contributed to this story.