ANCHORAGE, Alaska -- Republican U.S. Senate hopeful Joe Miller apologized on Twitter and a campaign staffer was told to exercise more caution Friday after someone in Miller's campaign sent a tweet that appeared to liken a possible party switch by Sen. Lisa Murkowski to prostitution.

The item posted on Miller's Twitter account Friday said, "What's the difference b/n selling out your party's values and the oldest profession?" The tweet linked to an online article speculating on whether Murkowski would run on the Libertarian Party ticket if she loses the GOP primary to Miller.

Murkowski's campaign responded by calling the tweet "disgusting" and demanding an apology, after which Miller issued another tweet that said: "Please accept my apologies. Staffer trying to encourage Libertarians not to sell out."

Alaska's GOP primary was held Tuesday but the Senate race between incumbent Murkowski and the tea party-backed Miller remains too close to call. With more than 20,000 ballots yet to be counted, Miller holds a narrow lead.

The initial tweet and link raised questions about whether Miller's campaign was comparing Murkowski's possible party switch to prostitution. Miller spokesman Randy DeSoto said the Twitter question was not directed at Murkowski but at the Libertarian Party in Alaska, and was posed by a staffer, not Miller. DeSoto says he's told the staffer to be more careful.

But Murkowski believed the intended target of the tweet was clear and demanded an apology from Miller for attacking her character and comparing her to a prostitute.

"Alaskans deserve better. This type of statement is inexcusable from someone who wants to represent our state," Murkowski said. "While I have been focused on the remaining ballots, the Miller campaign has launched yet another smear campaign against me. They lied about my record during the primary and now they have resorted to name-calling -- it's disgusting."

The senator said Alaskan values have never meant a "complete disregard for the truth or a lack of common decency" and Miller owes "all Alaskans, women, and my family an apology."

Murkowski campaign manager John Bitney, said, "This is a high-profile race that the entire nation is watching, and it is deplorable."

Bitney said he didn't know if Miller or one of his staffers sent the tweet but in the end it doesn't matter.

"The account has his name on it and he is responsible for it," Bitney said. "It represents him and his candidacy."

Meanwhile, the Fairbanks Daily News-Miner reported that Miller was involved in a three-car accident Friday at 8 a.m. No one was hurt. Trooper spokeswoman Megan Peters said two of the drivers weren't paying attention, but it was unclear if Miller was one of the drivers at fault.