"At this point we have no definitive evidence of the nationalities or identities of the perpetrators," State Department spokeswoman Jen Psaki said Monday.
In the past, federal officials and Somali-American leaders in Minneapolis have reported that Al-Shabaab has recruited young men there to go to Africa to fight.
U.S. President Barack Obama expressed condolences over the attack after a meeting on the sidelines of the U.N. General Assembly Monday. He didn't specify whether Americans had been involved, but he pledged U.S. support and described the situation as a matter of global concern.
"This, I think, underscores the degree to which all of us as an international community have to stand against the kind of senseless violence that these kinds of groups represent," Obama said.
The terrorist attack began at midday Saturday, Nairobi time, with an estimated 10 to 15 gunmen taking over the mall in what hospital volunteer Abiti Shah said witnesses told her was "like a Hollywood action scene."
"They just started firing in the air," Shah said, retelling the witness accounts.
A youth cooking competition was taking place at the mall at the time, and terrified shoppers fled for their lives as gunfire echoed through the building.
Witnesses said the gunmen went from store to store, shooting people, and then took hostages.
Survivor Bendita Malakia, a North Carolina woman who moved to Nairobi in July, told CNN affiliate WAVY that she took refuge behind the closed metal gates of a store with dozens of others.
"While we were back there, you could hear them methodically going from store to store, talking to people and asking questions," she said. "They were shooting, screaming. Then it would stop for a while and they would go to another store."
Al-Shabaab has claimed that the attackers targeted non-Muslims and vowed they would not negotiate for the hostages' lives. CNN security analyst Peter Bergen said the terrorists apparently took hostages only to prolong the siege and win more media attention.
Most of the dead were said to be Kenyans.
Six British citizens, two French nationals, two Indians and two Canadians, including a diplomat, also died, their governments said.
Those killed include:
• Elif Yavuz, a senior vaccines researcher for the Clinton Health Access Initiative based in Tanzania. Yavuz, a Dutch national, was pregnant and expecting her first child in October, according to Julio Frenk, dean of faculty at the Harvard School of Public Health. "Elif was brilliant, dedicated, and deeply admired by her colleagues, who will miss her terribly," the Clinton family said in a statement. The Dutch Foreign Affairs Ministry confirmed a 33-year-old Dutch woman had been killed.
• A major African poet, author and Ghanian statesman, Kofi Awoonor, Ghana's president said. Awoonor received his Ph.D. from New York's Stony Brook University and was a professor of literature there in the 1970s.
• The nephew of Kenyan President Uhuru Kenyatta and the man's fiancee.
• A Peruvian doctor, Juan Jesus Ortiz, who had previously worked for the United Nations Fund for Children and lived in Kenya doing consulting work, the country's Foreign Affairs Ministry said.