In a bid to contain the violence, Ahmed declared a state of emergency on Monday.
Asked if the US was afraid the government might collapse or be overwhelmed by attacks by fighters, Kelly replied: "We are concerned.
"We think that this government ... represents Somalia's best chance for peace, stability and reconciliation," he said.
"In addition to this threat to the government ... this kind of violence is causing real suffering for the Somalian people and it's just prolonging the chaos and preventing the country from getting on stable footing."
Kelly confirmed that the US organised an arms shipment made to the Somali government earlier this month, but did not confirm plans to train Somali forces in Djibouti.
The state department said it was providing the arms in accordance with UN Security Council resolutions.
The rebels used long knives to cut off a hand and a foot each from four young men in Mogadishu as punishment for theft, witnesses said.
"The horrific nature of such acts that were carried out in front of a crowd adds further injustice and dehumanizes these teenagers," said rights group Amnesty International.
Al-Shabab has carried out executions, floggings and amputations before, mainly in the southern port of Kismayu.
Movies and football matches are reportedly banned in areas it controls, and men and women cannot travel together on public transport.
The government has launched a series of attacks this month to drive the fighters out of Mogadishu but it has failed to make headway and is relying on African Union troops to protect the presidential palace, airport and seaport.