With 520 of 595 precincts reporting late Tuesday, Dill was leading her nearest opponent, former Secretary of State Matt Dunlap, 44.85 percent to 34.99 percent. Summers was ahead of second-place finisher Bruce Polquin, 30 percent to 22.64 percent the Bangor Daily News reported.
In claiming victory, Dill had a message for former Gov. Angus King, who is running as an independent to succeed Snowe, saying "to Angus King, bring it on baby."
King has said he knows he has a bull's eye on his back in the November election.
"It's not easy being the target," King, a Democrat-turned-Independent, told The Portland Daily Sun in a recent interview. "I'm prepared for that and I'll respond."