Corey Stewart, a hard-right firebrand and county official, captured the Republican nomination for Senate in Virginia on Tuesday night, dealing a blow to a party already struggling to hold on in an increasingly blue state that is key to Republican hopes of defending their House majority.
Mr. Stewart, who has attacked illegal immigration in heated language and fiercely defended the state’s Confederate monuments, edged Nick Freitas, a conservative state legislator, The Associated Press reported, with about 45 percent of the vote. He will take on Senator Tim Kaine, a Democrat, in November’s general election.
Mr. Stewart, who nearly seized the Republican nomination for governor last year, has savaged G.O.P. leaders in the state and has faced intense scrutiny for his associations with multiple white nationalist figures.
Republicans feared that having Mr. Stewart as their nominee against Mr. Kaine, the former vice-presidential nominee, will spur moderate voters and women to desert the party in droves, imperiling several contested House seats in the state.
Virginia Republicans, who have not won statewide in nearly a decade, were never optimistic about defeating Mr. Kaine, who has more than $10 million on hand. But their candidates may now find themselves captive to Mr. Stewart’s every utterance over the next five months — an unwelcome burden for lawmakers like Representatives Barbara Comstock and Scott Taylor, who were already endangered in their campaigns for re-election.
Mr. Kaine’s campaign immediately denounced Mr. Stewart, describing him in a statement as a “cruder imitation of Donald Trump who stokes white supremacy and brags about being ‘ruthless and vicious.’”
“Corey Stewart would be an embarrassment for Virginia in the U.S. Senate,” Ian Sams, a spokesman for Mr. Kaine, said in the statement.
The National Republican Senate Committee declined to comment on Mr. Stewart’s nomination.
In an emphatic display of the energy behind Democratic women in congressional races this year, Virginia Democrats nominated three women Tuesday night for the three most contested House seats in the state. They selected Abigail Spanberger, a former C.I.A. officer, to oppose Representative Dave Brat outside of Richmond, and Elaine Luria, a Navy veteran, to challenge Representative Scott Taylor in his Hampton Roads-based seat.
And in the state’s most vulnerable Republican-held district, Democrats selected State Senator Jennifer Wexton to oppose Representative Barbara Comstock. Ms. Comstock’s district, which stretches from Northern Virginia to the Shenandoah Valley, voted strongly against Mr. Trump in 2016 and rejected Republican candidates for the legislature and statewide offices last fall. Ms. Wexton won with the help of an endorsement from Gov. Ralph Northam, who carried the district by a double-digit margin in his campaign last year.
Democrats had previously selected Leslie Cockburn, a former journalist, in a convention as their nominee for the conservative-leaning Fifth District held by Representative Tom Garrett, a Republican who abruptly announced his retirement last month.
Primaries were also held Tuesday in South Carolina, North Dakota, Maine and Nevada, with the latter two featuring Democratic contests where long-serving women faced off against male opponents. Democratic women have fared well in many congressional primaries this year, but the Maine and Nevada races marked the starting line for a long season of more difficult primaries for female candidates for governor.
In South Carolina, Gov. Henry McMaster, a staunch Trump ally, was forced into a run-off — a vivid illustration that a Republican’s positive standing with the president does not necessarily transfer in local races.
Despite wielding a strong endorsement from Mr. Trump, Mr. McMaster, 71, could not reach the 50 percent level needed to avoid a run-off, The A.P. reported. He will face off against John Warren, a 39-year-old former Marine and first-time candidate, on June 26.
In Nevada, Democrats were closely watching a contentious primary between a pair of Las Vegas-area officials, Steve Sisolak and Chris Giunchigliani, which evolved into a proxy battle between former Senator Harry Reid and Hillary Clinton.
Mr. Sisolak entered the race first with the blessing of Mr. Reid, the former Senate majority leader who remains the de facto head of the Nevada Democratic Party, and he raised significantly more money than the progressive Ms. Giunchigliani. But she pulled into contention thanks in part to an infusion of money from outside groups, most notably Emily’s List, the group that backs Democratic women who support abortion rights. And over the weekend, Ms. Clinton intervened in the race, recording an automated call for Ms. Giunchigliani. Both Democratic hopefuls serve on the Clark County commission.
The winner will likely face Adam Laxalt, the 39-year-old state attorney general and son of former senator Paul Laxalt, who was expected to easily win the Republican primary.
Nevada will also have one of the marquee Senate races in the country this year, as Dean Heller is the only Republican senator in the country facing re-election in a state carried by Mrs. Clinton. Mr. Heller, who is in his first term, faced nominal opposition in his primary after Mr. Trump persuaded Danny Tarkanian, the son of the legendary Nevada-Las Vegas basketball coach, to drop out and run for the House. And thanks to Mr. Reid and other leading Democrats who helped clear the way, Representative Jacky Rosen also enjoyed little opposition in her bid to challenge Mr. Heller.
In Maine, where Democrats and Republicans were selecting their nominees for governor, a new system of voting promised to provide an atmosphere of uncertainty that could last for several days. Voters in the state were ranking primary candidates in order of preference, and using second- and third-place preferences to settle races in which no first-choice candidate achieves majority support. There is a crowded field of governor’s candidates in both parties and it is unlikely anyone will win based on the first round of preferences.
While races in most of the country have been defined by a candidate’s stance toward Mr. Trump, the race for governor in Maine has largely unfolded in the shadow of Gov. Paul R. LePage, an unpopular and deeply divisive Republican who has aligned himself with the White House.
On the Democratic side, the strongest candidates appeared to be Janet Mills, the state attorney general, and Adam Cote, a businessman and military veteran. But the race is unsettled enough that other candidates, like Mark Eves, a former speaker of the State House of Representatives, may have a chance to win.
The leading Republicans are Shawn Moody, a wealthy businessman, and Mary Mayhew, a former health official in the administration of Mr. LePage, who is leaving office at the end of the year.
Democrats in Maine were also selecting a nominee to challenge Representative Bruce Poliquin, a Republican from the state’s predominantly rural Second District.
The general election contest with Mr. Poliquin could be an important test of Democrats’ ability to win in Trump country: the president carried the district in the presidential race, picking up one of Maine’s four Electoral College votes because of the state’s unusual method of apportioning its votes.