After the Democrat Mark Kelly was declared the winner of his Senate re-election race in Arizona, the outcome of a tight race in Nevada will determine whether Democrats can secure a majority in the upper congressional chamber without having to hold their breath until the December runoff in Georgia.

The race between Nevada’s Democratic incumbent, Catherine Cortez Masto, and her Republican challenger Adam Laxalt, the state’s former attorney general, got even closer on Saturday when a batch of counted votes were reported. Just 862 votes make up Laxalt’s lead. About 25,000 mail-in ballots and 15,000 ballots that need “curing”, or correcting by the voter, have yet to be reported.

Laxalt tweeted on Saturday morning that that the race appeared to be inching away from his favor.

“We are up only 862 votes. Multiple days in a row, the mostly mail-in ballots counted continue to break in higher Dem margins than we calculated. This has narrowed our victory window,” he said.

The bulk of the remaining ballots will come from Clark county, home to largely Democratic Las Vegas. Drop-off and mail-in ballots for the race so far have also favored Cortez Masto, upping the chances that she will keep her seat.

If Democrats win this seat in Nevada, they – along with Democratic-leaning independents – will have 50 seats in the Senate. The vice-president, Kamala Harris, who presides over the Senate, can serve as a tie-breaker in any 50-50 votes.

Many of the remaining ballots are expected to be counted and reported by Saturday, though the deadline for counting the remaining ballots is on Tuesday.

Even after the Nevada race is called, one race remains in Georgia, where the Democratic incumbent, Raphael Warnock, and his Republican challenger, the former football star Herschel Walker, will head into a runoff election on 6 December. Republicans have clinched 49 seats in the Senate so far.

Meanwhile, control of the US House of Representatives remained in flux on Saturday, with 25 races yet to be called on Saturday afternoon. Republicans have a lead over Democrats, with 211 seats to Democrats’ 199. Though Democrats are still down 12 seats compared with Republicans, the party has had a surprisingly strong turnout this midterm election. To have the majority, a party needs 218 seats.

House races still need to be called in eight states, including in Arizona, California and Washington, where votes for close races are still being counted. The political analyst Dave Wasserman of the Cook Political Report said in a tweet on Saturday that Democrats would need to win each of six toss-up races in order to get a majority.