The US recognizes Libya’s rebel government as one of the representatives of Libyans, not the only representative. Washington’s goal is to see Libyan leader Col. Muammar Qaddafi step down and for the rebel council and the government in Tripoli form one body to govern the country.
But the US remarks on the council could be easily misunderstood because, as US Assistant Secretary of State for Near Eastern Affairs Jeffrey Feldman noted in the Washington Post, the council is the de facto sole representative right now. The US asked the Libyan Embassy in Washington to close its doors earlier this year. The only US representatives in Libya are in Benghazi, the rebel capital, and not in Tripoli.
Britain, too, has stopped short of full recognition of the rebel government, although it has been in direct contact with them, like the US.