Sen. Lisa Murkowski (R-Alaska) declined to run for Senate as a Libertarian on Tuesday, but said she would decide whether or not to launch a write-in bid on Friday.

The incumbent senator, who lost a primary election to Tea Party-backed candidate Joe Miller last month, said she has received an "outpouring of support" from people in her state but is still undecided as to whether she will attempt to keep her Senate seat.

"After meeting with the Libertarian candidate last week and considering that option, I cannot in good conscience seek the Libertarian nomination," she said.

Murkowski accused the Tea Party Express, which poured $500,000 into Miller's campaign, of hijacking the Alaska Republican Party, but said she "is not going to quit my party.

"I will not wrap myself in the flag of another political party for the sake of election at any cost," she said.

Murkowski remained in Alaska through Monday while exploring her options to remain in the race, despite the fact she orignally conceded the race. Her campaign said she returned to Washington on Tuesday.

The Alaska senator said she would decide on carrying out an independent write-in bid by the end of the week even though she has only received tepid support for the idea from her Senate GOP colleagues.

“I recognize that not seeking the Libertarian’s position on the ballot leaves me with the more difficult task of running a write-in campaign should I decide to continue in the race," she said. "I will continue to seek advice from my fellow Alaskans about what is best for the state’s future and announce a decision by Friday."

Tea Party Express spokesman Levi Russell responded that Murkowski "is a sore loser" and that her post-election behavior shows "nothing but contempt for the people of Alaska."

"It's time for her to start doing the right thing by volunteering to help Joe Miller win this election for the Republican Party in November," Russell said.

-- This post was updated at 8:24 p.m.