The Pentagon confirmed that US forces carried out attacks on Monday, the first overt US military action in Somalia since 1994, as part of a wider offensive involving Ethiopian aircraft.
Officials said Monday's strike was aimed at a suspected al-Qaeda cell and Fazul Abdullah Mohammed, a man wanted by the FBI in connection with the bombings of US embassies in Africa in 1998, was reported to have been killed in the attack.
The US involvement has provoked international criticism, but the US defended its actions.
A defence spokesman said: "We have a concern that those terrorist elements operating in Somalia not be allowed to flee."
Abdirizak Hassan, the Somali president's chief of staff, was reported on Wednesday as saying that at least three US air strikes had been carried out since Monday and one government source said four new US strikes hit areas around Ras Kamboni, close to the Kenyan border.
But the Pentagon has acknowledged only Monday's attack, contradiciting Somali government claims.
Some sources have suggested that Ethiopia conducted the additional attacks.
The US aircraft carrier USS Eisenhower, from which raids by fixed-wing fighters may be called, continues to be positioned off Somalia's coast.