(CNN) -- Republican Senate candidate Joe Miller said late Sunday he is dropping his opposition to incumbent Lisa Murkowski being certified as winner in the Alaska Senate race, but will continue with a federal lawsuit.
"After careful consideration and seeking the counsel of people whose opinion I respect and trust, I have decided that the federal case must go forward. The integrity of the election is vital and ultimately the rule of law must be our standard," Miller said in a statement. "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."
Last week, the Alaska Supreme Court ruled against Miller in his appeal, denying his claim that state law was not followed on counting write-in votes.
In the ruling, the Alaska Supreme Court affirmed the decision of the superior court, saying, "There are no remaining issues raised by Miller that prevent this election from being certified." At the time, a spokesman for Miller's campaign said they were "disappointed" with the decision.
"We are disappointed the Alaska Supreme Court has ignored the plain text of Alaska law and allowed the Division of Elections to effectively amend the state election code without even giving the public an opportunity for notice and comment," Miller spokesman Randy DeSoto said in a statement Wednesday.
The Alaska Division of Elections had already said that the state would move forward to ask the judge to lift the injunction on certifying the election unless the Miller campaign filed an appeal by Monday -- which it will now not do.
The Murkowski campaign anticipated further appeals by Miller.
"We ... anticipate that Joe (Miller) will continue to pursue his baseless claims in federal court until his money runs out," Murkowski spokesman Kevin Sweeney said in a statement last week.
After the election in November, Miller filed a challenge against the Division of Elections to ensure the state law, which calls for write-in votes to match the name of the candidate, was followed. He has argued that Alaska law does not allow the counting of misspelled names on write-in ballots.
However, the Division of Elections set guidelines before counting began that allowed for a voter's intent to be considered when determining whether to count a ballot for a write-in candidate.
Murkowski launched a write-in bid following her loss to Miller, a Tea Party favorite, in the state's August 24 Republican primary.
In the original superior court decisions, a judge ruled that Miller did not provide proof of election official fraud, or that "there would be a sufficient change to the election results if these claims were true."
The Associated Press called the race for Murkowski last month when she had a 10,328-vote lead over Miller, a figure that includes the 8,159 ballots contested by Miller observers. Not including those ballots, she has a 2,169-vote lead.
CNN's Steve Brusk contributed to this report