SEATTLE — The lieutenant governor of Alaska, Byron Mallott, resigned abruptly on Tuesday after making what Gov. Bill Walker, a political Independent, called “inappropriate” but unspecified comments.

The resignation threw an already tight re-election effort by Mr. Walker into even more uncertain territory with only a few weeks before voting begins.

Mr. Mallott, 75, is the state’s most prominent Native Alaskan politician, a member of the Tlingit people, and has been a hugely popular figure in rural tribal areas of the state. As a Democrat, he was also part of an unlikely political marriage with Mr. Walker, a former Republican who left his party to run as an Independent in 2014.

In his first term, Mr. Walker repeatedly referred to Mr. Mallott as his partner in dealing with a huge budget deficit that has required painful cuts to state programs and a reduction in payments to Alaskans from a fund created by decades of oil tax revenues.