The Associated Press projected the two as advancing to the March 31 runoff.
Other Republicans, including Rep. Bradley Byrne and former state Supreme Court chief justice Roy Moore, significantly trailed the leaders, leaving them on course to miss the runoff.
The race has attracted significant national attention for its importance in the battle to control the Senate — it is the GOP’s best chance to wrest a seat from Democrats this year — and for Sessions’s decision to enter the contest after an ignominious exit as attorney general in 2018.
Throughout the campaign, Sessions had to confront his difficult relationship with President Trump, who openly attacked him starting in 2017 when he decided to recuse himself from any role in the federal investigation into Russian interference in the 2016 election, paving the way for the appointment of special counsel Robert S. Mueller III.
But Sessions attempted to remind voters of his early support for Trump’s presidential ambitions and his role as an intellectual godfather of the anti-immigration, anti-free-trade governing agenda — even as Tuberville and Byrne cast themselves as more reliable supporters of the president.
Trump has so far remained silent on the race, and Republicans in both Alabama and Washington are speculating whether he might now get involved to block Sessions.
“If it is a runoff, we don’t know what will happen,” Sen. Richard C. Shelby (R-Ala.) said this week. “I would hope he wouldn’t [get involved], but if he does, we’ll see.”
Byrne took about a quarter of the vote, according to early returns. Moore, the GOP nominee in a 2017 special election in which allegations of his sexual misconduct toward young girls in the 1970s upended the race and paved the way for the surprise victory of Democrat Doug Jones, was in single digits.
The eventual Republican nominee is expected to have the upper hand over Jones in the reliably conservative state.
Meanwhile, in North Carolina, Democrats nominated a centrist favorite of national party leaders to take on GOP Sen. Thom Tillis in what promises to be a much more competitive race.
Cal Cunningham, a former state senator and Army veteran, outpolled state Sen. Erica Smith, who had campaigned on a more liberal platform that included supporting the Green New Deal climate plan.
Those views, which national leaders of both parties saw as troublesome in a swing-state general-election matchup, prompted a GOP super PAC affiliated with Senate Majority Leader Mitch McConnell (R-Ky.) to spend nearly $3 million boosting Smith’s candidacy. Smith disavowed the GOP support, but Cunningham and allied groups boosted their own spending in turn — posting a combined $14 million in primary spending.
Incomplete returns showed Cunningham winning 57 percent of the vote with 99 percent of precincts reported.
The Alabama and North Carolina races were among several closely watched congressional primaries that could have significant implications for control of the Senate and the shape of each party.
Texas hosted another Senate primary of note, with five Democrats running credible campaigns for the chance to face three-term GOP Sen. John Cornyn later this year.
Military veteran M.J. Hegar, who ran a strong but unsuccessful 2018 House campaign in a traditionally GOP district, had won the endorsement of the Democratic Senatorial Campaign Committee and appeared to qualify for a May 26 runoff.
But it remained unclear late Tuesday which Democrat she would face: Labor organizer Cristina Tzintzún Ramirez, state Sen. Royce West and Houston City Council member Amanda Edwards were in a close contest for second place with about half of statewide precincts reported.
Also in Texas, two expensive and hotly contested House primaries tested the willingness of voters in both parties to reward pragmatism over ideological purity.
In a South Texas district centered on the border town of Laredo, Democratic Rep. Henry Cuellar faced a fierce challenge from Jessica Cisneros, a 26-year-old immigration lawyer who attracted support from key allies on the political left, such as Sen. Bernie Sanders (I-Vt.), Sen. Elizabeth Warren (D-Mass.) and Rep. Alexandria Ocasio-Cortez (D-N.Y.), as well as Emily’s List, which backs female Democratic candidates who support abortion rights.
The two campaigns and outside groups have combined for over $6 million in spending — an overwhelming tally for a largely rural, heavily Latino district — and Cisneros’s challenge has caught the attention of other veteran incumbents who are facing more-liberal primary opponents.
With about a third of precincts reporting, Cuellar held a 10-point lead, and while a spokesman, Colin Strother, declared the campaign “cautiously optimistic,” he did not declare victory Tuesday.
Another intraparty challenge rocked a district 400 miles north, this one targeting GOP Rep. Kay Granger, a former Fort Worth mayor who has risen to become the top Republican on the House Appropriations Committee. Her handling of that role drew attacks from businessman Chris Putnam, who found common cause with the Club for Growth, the fiscally conservative national activist group that invested more than $1 million to oust Granger.
Granger, who won Trump’s endorsement, was headed toward a roughly 20-point victory with 85 percent of precincts tallied Tuesday.
Trump’s endorsement appeared to have less of an effect in another notable Texas House race: Former White House physician Ronny L. Jackson, backed by Trump, was in a distant second place with about one-third of precincts in the Panhandle-based 13th Congressional District reporting. He trailed cattle industry lobbyist Josh Winegarner, who has the backing of retiring Rep. Mac Thornberry (R). The two could meet in a May 26 runoff.
Several key House races in California were likely to remain unsettled Tuesday night — and the results could remain uncertain for weeks as state authorities continue counting mailed ballots that had to be postmarked by primary day.
Among the highest-profile races was a special election in the 25th Congressional District north of Los Angeles to replace Democratic Rep. Katie Hill, who resigned last year after admitting to having a sexual relationship with a campaign aide.
Key Democratic groups coalesced behind Christy Smith, a member of the State Assembly, but she faced a liberal challenger in activist Cenk Uygur, as well as strong Republican competition from former congressman Steve Knight and businessman Mike Garcia — one of whom is expected to compete in a May 12 runoff against Smith.
Also running, but not expected to advance, is George Papadopoulos — a volunteer on the 2016 Trump campaign who became a key figure in the probe into Russian interference in the 2016 election and later pleaded guilty to making false statements to federal agents.
In California's 50th Congressional District, north of San Diego, former Republican congressman Darrell Issa is hoping to return to the House two years after retiring in a neighboring district. He has been locked in a heated and nasty race with former San Diego City Council member Carl DeMaio for a spot in a likely runoff against Democrat Ammar Campa-Najjar, who fell short in his 2018 bid to unseat GOP Rep. Duncan D. Hunter.
Hunter resigned from the House in January after admitting to a federal campaign finance felony.
Other notable California contests include a couple of probable 2018 rematches: In the Central Valley’s 10th District, former GOP representative David Valadao is hoping to reclaim the seat he held for three terms from Democratic Rep. TJ Cox. And in Orange County, former state legislator Young Kim is making a second attempt to beat Democratic Rep. Gil Cisneros after losing one of 2018’s closest House races.
In California, the top two vote-getters advance to the general election, no matter what party.