Republicans have captured at least 210 House seats, Edison Research projected, eight short of the 218 needed to wrest the House away from Democrats and effectively halt President Joe Biden's legislative agenda.
While Republicans remain favored, there were 33 House contests yet to be decided - including 21 of the 53 most competitive races, based on a Reuters analysis of the leading nonpartisan forecasters - likely ensuring the final outcome will not be determined for some time.
Meanwhile, the fate of the Senate was far less certain. Either party could seize control by winning too-close-to-call races in Nevada and Arizona, where officials are tallying thousands of uncounted ballots.
Even a slim House majority would allow Republicans to shape the rest of Biden's term, blocking priorities such as abortion rights and launching investigations into his administration and family.
The party in power - presently the Democrats - historically suffers heavy casualties in a president's first midterm election and Tuesday's results suggested voters were punishing Biden for the steepest inflation in 40 years.
But Tuesday's results also suggested voters were lashing out against Republican efforts to ban abortion and to cast doubt on the nation's vote-counting process.
A White House official said Biden spoke by phone with Republican House leader Kevin McCarthy, who announced earlier in the day his intention to run for speaker of the House if Republicans control the chamber.
"The American people have made clear, I think, that they expect Republicans to be prepared to work with me as well," Biden told a news conference.
If McCarthy is the next House speaker, he may find it challenging to hold together his fractious caucus, with a hard-right wing that has little interest in compromise.
Republicans are expected to demand spending cuts in exchange for raising the nation's borrowing limit next year, a showdown that could spook financial markets.
Control of the Senate, meanwhile, would give Republicans the power to block Biden's nominees for judicial and administrative post.
Thousands of votes still remained uncounted in the two closely competitive states of Arizona and Nevada. Election officials in Maricopa County, Arizona's most populous, said it could take until at least Friday to tally all votes there.