Senator Ted Stevens of Alaska fell slightly behind his Democratic rival, Mark Begich, on Wednesday, as ballot counting continued in one of the nation’s most closely fought Senate races.

In an initial count after Election Day, Mr. Stevens led Mr. Begich, the mayor of Anchorage, by 3,257 votes.

Mr. Begich led Mr. Stevens by just 814 votes after about 57,000 additional ballots were counted on Wednesday. So far, about 279,000 votes have been counted in the Senate race, and about 35,000 more remain to be counted. It could be next week before the count is complete.

Republicans claimed then that traditional voting patterns among absentee voters favored Mr. Stevens’s holding on to win, but Mr. Begich countered that he had made a concerted effort to win early and absentee voters. Initial counts of those ballots appear to be favoring Mr. Begich.