Residents said three people were wounded when a shell fell near houses nearby.
Al-Shabaab, a splinter group of Somalia's Islamic Court Union (ICU) movement, said its fighters had fired the mortars.
"We fired on the airport to target the so-called democratic congressman sent by Obama," Sheikh Hussein Ali, an al-Shabaab spokesman, told the Reuters news agency.
The congressman's visit came a day after a US merchant captain was freed from Somali pirates after the US Navy ended a five-day standoff, killing three of the four who had been holding the American hostage.
The incident marked the first time an American had been taken captive in the recent wave of pirate attacks seen off the Horn of Africa since 2006.
US foreign policy towards Somalia has been tenuous ever since 18 US soldiers were killed in a battle in Mogadishu in 1993.
Somalia's civil conflict, lawlessness and widespread poverty have led to the return of pirates to the waters off the Horn of Africa after nearly two decades of relative calm.
Last year, the UN Security Council took steps aimed at curbing Somalia's pirates by authorising navies to follow pirates into Somalia's territorial waters and allowed land operations against known pirate havens.
Arms race fears
Some US military officials have expressed caution at the idea of becoming more aggressive against pirates, or increasing the number of warships on patrol.
Thad Allen, a US coast guard spokesman, said that arming ships' crews was unpopular with shipping companies which are concerned about entering an arms race with pirates and being held liable for the weapons.
"That's not what these mariners are trained to do," Allen said. "What you really have to have is a co-ordinating mechanism that ultimately brings these pirates to court."
In the last three weeks, there have been 18 or 19 piracy attempts in the Gulf of Aden and the Somali Basin.
Pirates are believed to have attacked nearly 150 ships and collected millions of dollars in ransom money in 2008.