"It poses a threat to Kenya, poses a threat to the stability of Africa and beyond. So this is an area where we're going to work even more closely together," she added.
Al Jazeera's Mohammed Adow said: "It continues to be hell for the people who live in Mogadishu [the Somali capital].
"Violence and continued violence is the norm on the streets.
"People are increasingly becoming fearful of continuing to live in their houses ... and they are only reliant on a trickle of aid."
The US has already offered military aid to Mogadishu, including more than 40 tonnes of ammunition and training for security forces.
Somalia has suffered from lawlessness and violence since 1991, when the country descended into civil war.
Ahmed, who was elected in January under a UN-brokered process, is part of Somalia's 15th attempt to set up a central government in nearly two decades.
Clinton's meeting with the president is also expected to tackle a rise in piracy off Somalia's coast, where vital shipping lanes connecting Asia and Europe have become the target of hijackers claiming millions of dollars in ransom.
Earlier this week Australian police said they had uncovered a plot to attack an army base in Sydney by men with alleged links to al Shahaab.
Washington has accused the group of being al Qaeda's proxy in Somalia.
Earlier on Thursday Clinton visited a memorial in Kenya honouring 236 people killed in the 1998 attacks on US embassies there and in Tanzania.
The US says some of those behind the attacks, which were linked to al Qaeda, are sheltering in Somalia.
The US secretary of state, who is on a seven-nation trip in Africa, said earlier that the growth of business and trade on the continent depends on good governance and solid democracy.
Clinton told regional leaders on Tuesday at a conference in Nairobi that political transparency would provide the basis for economic growth.
"True economic progress in Africa will depend on responsible governments that reject corruption, enforce the rule of law and deliver results for their people," she said.
"This is not just about good governance - it is also about good business."
Mwai Kibaki, Kenya's president, and Raila Odinga, the country's prime minister, were present at the conference, which was examining a US trade law aimed at boosting US imports of products made in Africa.
But Clinton criticised Kenya's leadership for not implementing reforms that formed the basis of a power-sharing deal agreed after deadly post-election fighting in 2007, in which at least 1,000 people were killed in clashes between supporters of Kibaki and Odinga.
Kenya is the first stop on Clinton's seven-nation tour of Africa. She is set to visit South Africa, Angola, the Democratic Republic of Congo, Nigeria, Liberia and Cape Verde.