Democrat Jon Tester defeated incumbent Republican Conrad Burns by fewer than 5,000 votes, according to US networks ABC and NBC.
Both NBC and ABC reported 49 percent for Tester and 48 percent for Burns, with 99 percent of precincts reporting.
In Montana, Tester told CNN that he was declaring victory.
In Virginia, where the Democratic challenger Jim Webb also holds a slight lead, it could take weeks to get a result if a recount is ordered, officials said.
A spokesman for the Republican incumbent, George Allen, on Wednesday would not concede defeat and vowed to ensure that every vote was counted.

Copyright AFP (Agence France-Presse), 2006