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Ms. Sinema, a former state senator, had a narrow lead on election night that made the race too close to call. But she slowly improved that advantage as more ballots were tallied in recent days, and now has an almost 6,000-vote edge that is too much for her opponent to overcome, AP says.

In California, Democrat Ami Bera increased his lead over GOP Rep. Daniel E. Lungren to almost 1,800 votes. The challenger led the longtime incumbent by fewer than 200 votes late last week.

The race for the Sacramento-area district, which is nearly split between registered Democrats and Republicans, was among the most fiercely contested in the nation, and attracted more than $8.3 million in spending by outside groups.

In Utah, Democratic Rep. Jim Matheson appears to have won a tight race over GOP challenger Mia Love, who conceded defeat. But with only about 2,600 votes separating the two and some provisional and mail-in ballots yet counted, major news outlets haven’t called the race.

In another race too close to call, California Democrat Scott Peters increased his lead over seven-term Republican Rep. Brian P. Bilbray to more than 1,300 votes. And in North Carolina, Democratic Rep. Mike McIntyre holds a 420-vote lead over Republican challenger David Rouzer.

In Louisiana, the race between two sitting GOP House members, Reps. Charles W. Boustany Jr. and Jeffrey M. Landry — pitted against each other because of redistricting — will extend a few more weeks as the two were forced into a runoff election after neither got a majority victory.

This article is based in part on wire-service reports.