JUNEAU, Alaska (AP) — Alaska Gov. Bill Walker said Thursday his re-election campaign is moving ahead but is taking it "a day at a time" after being rocked this week by the abrupt resignation of Lt. Gov. Byron Mallott.

Mallott resigned Tuesday over what Walker has described as an inappropriate overture to a woman. Mallott apologized though few details have been released. Walker said he is honoring the wishes of the woman involved.

Walker campaign manager John-Henry Heckendorn has said the campaign was in talks with Democratic rival Mark Begich about a "path forward for Alaska," but declined to elaborate when asked about it Thursday. Begich's campaign manager has not returned messages.

Walker is a Republican-turned-independent who was elected with Democratic support in 2014. He is locked in a tough three-way re-election fight. Some Democrats and independents have worried that he and Begich will split the vote, giving the race to Republican Mike Dunleavy, the presumed front runner.

During a debate Thursday, Dunleavy asked Begich if he was in negotiations with Walker for one of them to drop out before the Nov. 6 election.

"I'd like you to drop out," Begich said to laughter. Pressed further by Dunleavy, Begich said: "There's no deals."

Walker said the Republican Party contacted him to be their candidate after Dunleavy had filed. "There's all sorts of conversations going on out there," he said.

Tuckerman Babcock, chairman of the state GOP, said he assumed Walker was joking.

He said Walker's chief of staff, Scott Kendall, had asked if Walker would be welcomed to run or given a fair shot if he were to run as a Republican. Babcock said he told him Walker was free to file as a Republican if he wished. Babcock chalked up the inquiry to due diligence on behalf of Walker's people as Walker weighed his options.

The teaming of Walker and Mallott in 2014 was billed as a "unity" ticket; Mallott is a Democrat. Their partnership was a central element of Walker's first term.

During an Alaska Federation of Natives conference speech in Anchorage Thursday, Walker described Mallott as his "brother and my closest friend and my soul mate and that will not change."

Mallott did the right thing by taking responsibility, he said, adding later that his administration respects and believes women.

Some Walker supporters have wanted him to be clear about his campaign plans with early voting starting Monday.

Valerie Davidson, who preceded Walker on the Alaska Federation of Natives conference stage with a rousing speech Thursday, replaced Mallott as lieutenant governor and as Walker's running mate.

At one point Walker told reporters Thursday the campaign was "full steam ahead." Later, he was more measured.

"We're going to play it a day at a time, see what happens, where we are," he said. "At this point, I don't have any indication that anything's going to change."

___

Associated Press reporter Mark Thiessen contributed from Anchorage, Alaska.

Copyright 2018 The Associated Press. All rights reserved. This material may not be published, broadcast, rewritten or redistributed.