Ali Hussein Nur, a district commissioner, told Reuters news agency: "Since the American government admitted bombing our town, where people and livestock were killed and properties damaged, it must pay compensation."
The exact toll from Monday's attack is unclear.
Nur said on Monday that six people were killed, but Fatuma Omar, a local resident, said on Tuesday that only four people were wounded.
The US said on Tuesday that it was targeting Saleh Ali Saleh Nabhan, a Kenyan suspected in the 1998 bombings of two US embassies in Africa.
FBI statement
Richard Kolko, an FBI spokesman, said: "Saleh Ali Saleh Nabhan is on the FBI's 'seeking information list' and is wanted by the FBI for questioning in connection with the 2002 attacks at the Paradise Hotel and the unsuccessful surface-to-air missile attack against an Israeli airliner in Kenya."
Earlier on Monday a Pentagon spokesperson said the attack was against "a known al-Qaeda terrorist" but did not specify who.
Kolko said he could not confirm whether Nabhan had been hit in the strike and referred questions to the Defense Department.
Officials have said for several years that ungoverned areas of Africa are a breeding ground for terrorist groups.
Meanwhile, congressional auditors said on Tuesday that the US needs a comprehensive new strategy for Somalia.