Mr. Trump denounced “hatred, bigotry and violence — on many sides” and argued that many of the protesters who staged a torchlight march to protest the removal of a statue of Robert E. Lee were “very fine people.”

One of the counterprotesters, Heather Heyer, 32, was killed when a white nationalist demonstrator drove a car into a crowd. Two Virginia State troopers died when their helicopter crashed while monitoring the violence that swept through the usually sedate college town.

The House version of the resolution, introduced by Republican and Democratic House members from Virginia, asks Mr. Trump to “use all resources available to the President and the President’s Cabinet to address the growing prevalence of those hate groups in the United States.”

In a rare show of bipartisan unity, Speaker Paul D. Ryan of Wisconsin and Senator Mitch McConnell of Kentucky, the majority leader, introduced the measure as a joint resolution, which requires a presidential signature. Two Republican congressional aides involved in the process said the intent was to put the president on the record calling out white racism by name.

The text doesn’t include any reference to counterprotesters.

It also calls on Attorney General Jeff Sessions to “investigate thoroughly all acts of violence, intimidation, and domestic terrorism by White supremacists, White nationalists, neo-Nazis, the Ku Klux Klan, and associated groups” and to “improve the reporting of hate crimes” to the F.B.I.