PORTLAND, Maine (AP) — Republican Charlie Summers and Democrat Cynthia Dill won their crowded primary elections Tuesday in the race for Republican Sen. Olympia Snowe’s soon-to-be-empty seat, setting the stage for a three-way race with a popular former governor that could shift the balance of power in the U.S. Senate.

The Republican and Democratic nominees will face Angus King, a former two-term governor, and several other independents in an important race that could shift the balance of power in the closely divided U.S. Senate.

Summers said winning the general election will be a chore, but he thinks King’s record as governor of increasing government spending and leaving his successor with a $1.5 billion deficit will be his downfall.

‘‘Once Angus’ record is out, it will speak for itself and I think we can be successful,’’ Summers said.

For her part, Dill said the Democratic Party is ready for somebody who will stand up and be a strong voice in Washington for the middle class and small businesses. She also had a message for King: ‘‘Bring it on.’’

‘‘Democrats are ready to have a torchbearer who states very clearly and articulately what the Democratic core values are and not try to fudge and play to everyone in the political spectrum,’’ she said.

Snowe took the political establishment by surprise when she announced Feb. 28 that she wouldn’t seek a fourth term, citing partisan polarization and political gridlock in the Senate.

All told, 10 Republicans and Democrats were vying against each other in primaries Tuesday.

Scott D'Amboise, who had intended to challenge Snowe in a primary, was soon joined by five other Republicans aiming for the spot. Big-name Democrats like U.S. Reps. Chellie Pingree and Mike Michaud and former Gov. John Baldacci considered joining the race but opted out, leaving four other Democrats.

Joining D'Amboise, a small businessman from Lisbon Falls, on the Republican ballot were Summers, the secretary of state from Scarborough; Bruce Poliquin, state treasurer from Georgetown; and Rick Bennett, a former Senate president and CEO of a corporate watchdog firm from Oxford, along with Attorney General William Schneider of Durham and Debra Plowman of Hampden, state senator and co-owner of a garage door business.

Democrats on the ballot were Dill, a state senator from Cape Elizabeth, and Matthew Dunlap, former secretary of state from Old Town, along with Rep. Jon Hinck of Portland and Ben Pollard, a Portland homebuilder.

Tuesday evening, Summers was leading with 30 percent of the vote followed by Bruce Poliquin with 23 percent, with 79 percent of the state’s precincts reporting in unofficial returns in the GOP primary. In the Democratic primary, Dill had 45 percent to 35 percent for Dunlap.

King, who wasn’t even on Tuesday’s primary ballot, cast a long shadow on the campaign.

‘‘For any of these candidates to knock him off is going to take a monumental effort,’’ said Mark Brewer, political science professor at the University of Maine.

Republicans were all but assured of holding onto the seat before Snowe’s departure. As an independent, King insists he can bridge the gulf between the parties. Senate Democrats currently hold a 51-47 majority with two independents who caucus with them.

In the primary campaign, Republicans focused much of their attention on King, a former Democrat, attacking him as a free-spending liberal and thinly disguised Democrat-in-independent’s clothing.

Democrats battled to show they that can produce a candidate strong enough to take on the Republican nominee as well as King, a self-made millionaire. Also on the ballot will be three other independents, including businessman Steve Woods of Yarmouth and tea party activist Andrew Ian Dodge.

Summers touted his resume. He’s served in the Legislature, he’s a small business owner, he worked for Sen. Olympia Snowe, served as regional administrator of the Small Business Administration and, as a Navy reservist, spent time in both Iraq and Afghanistan

‘‘It proved I wasn’t a one-dimensional candidate,’’ he said.

Cynthia Dill has ascended from her local town council to the state House of Representatives to the state Senate. Along the way, she’s taken shots from Republicans who have labeled her as an ultraliberal. She calls herself progressive.

She described King’s candidacy ‘‘some sort of political or social experiment’’ and said she looks forward to debating him before the November election.