U.S. District Court Judge Ralph Beistline, who is hearing the Republican nominee's challenge, had said earlier he would probably lift his order staying certification, letting Murkowski be sworn in for a new term Jan. 5, the Anchorage Daily News reported.
"I have decided that the federal case must go forward," Miller said in a statement. "The integrity of the election is vital and ultimately the rule of law must be our standard. Nevertheless, I have also decided to withdraw our opposition to the certification of the election, ensuring that Alaska will have its full delegation seated when the 112th Congress convenes next month."
Miller initially challenged Murkowski's write-in victory in federal court, but Beistline ruled he had to go to state court first. Miller lost in state Superior Court, and the Alaska Supreme Court unanimously backed the decision.
Beistline had given Miller until Monday morning to file motions continuing his case. The state has until Wednesday to respond.
Duggar sisters unveil Christian dating rules in new book
Attkisson leaves CBS News, reportedly over network's 'liberal bias'