In Arizona and Nevada, Republicans’ path to victory appeared to narrow, though both races remain close. The G.O.P.’s odds of success are greater in the House.

Democrats grew increasingly optimistic on Thursday that they would hold on to their control of the Senate as votes were counted in Arizona and Nevada, after chalking up vital victories in New Hampshire and Pennsylvania and watching the race in Georgia head to a runoff election in December.

Republicans need to flip at least one seat to take control of the chamber, but their path appeared to be narrowing on Thursday, with Democrats holding a shrinking but durable lead in Arizona and picking up mail ballots in Nevada at a rate that seemed to give the party a slight edge. The G.O.P.’s odds of success were greater in the House, where the party had won or was leading in the races for 221 seats, just three more than it needs to retake the chamber.

In the Senate, “I think we have a very legit chance of expanding our majority from 50 to 51,” said Senator Tim Kaine, Democrat of Virginia, pointing to the data in Arizona, Georgia and Nevada. “Very few people would have given us that chance before the election.”

Senator Chuck Schumer, the majority leader, has been checking with Democrats in Arizona and Nevada every few hours, a spokesman said, emerging more optimistic with each phone call. On Wednesday, Mr. Schumer told reporters that he was “feeling good” about keeping the Senate.

If Democrats prevail in Arizona and Nevada, they will clinch control of the Senate even before the Georgia runoff contest. This would lower the stakes of that Dec. 6 rematch between Senator Raphael Warnock and Herschel Walker, who earned significantly fewer votes than Gov. Brian Kemp on Tuesday. But it’s not clear whether that possibility would benefit Democrats or Republicans. Neither side is taking any chances: Mr. Schumer has begun raising money for Mr. Warnock, and Senate Republicans are doing the same for Mr. Walker.

“For Democrats to be in this position right now, every single thing had to go right for them on election night,” said Jessica Taylor, a Senate analyst at The Cook Political Report With Amy Walter. “And every single thing went right for them on election night.”

She added, referring to Arizona and Nevada, “I do think they’ll win both races.”

In Arizona, Senator Mark Kelly was comfortably ahead of Blake Masters, his Republican opponent, with 70 percent of ballots counted. Mr. Kelly’s lead of five percentage points was likely to shrink, Democrats said, but not by enough to put Mr. Masters on top. On Wednesday, Mr. Kelly won a batch of mail-in votes in Maricopa County, the state’s largest and home to Phoenix, by 15 points. Approximately 600,000 votes are left to be counted.

In an email to supporters on Thursday, the Masters campaign said it had seen “troubling” issues during the election and asked for contributions: “We’re expecting a contested road forward and legal battles to come.”

The race in Nevada, which was among the states hit hardest by the pandemic and by inflation, is much closer. Polls suggested for months that Senator Catherine Cortez Masto was struggling and that she would need to lean heavily on the turnout operation built by her predecessor, Senator Harry Reid. This year was the first midterm election in which Nevada sent every voter a mail-in ballot, adding a new wrinkle of uncertainty.