Washington (CNN) -- A State Department spokesman put the death toll from Sunday's trio of bombings in Uganda's capital city of Kampala at 76 Tuesday, raising the count by two.
"As of today, we understand, the number killed is 76, including the one American that has been identified," P.J. Crowley told reporters.
The five wounded Americans have been evacuated, two to Johannesburg, South Africa, and three to Nairobi, Kenya, he said.
Diplomatic security agents and "a small number" of FBI agents were in the city, he said. A larger FBI contingent was expected to depart Tuesday for Uganda at the request of Ugandan authorities to help in the investigation, he said.
The increased death toll came a day after a Somali Islamist militant movement claimed responsibility for the bombings at two locations where crowds had gathered to watch the World Cup final.
"And the best of men have promised and they have delivered," said an Arabic statement issued by Al-Shabaab's press office and obtained by CNN. "Blessed and exalted among men -- (taking) full responsibility. ...We wage war against the 6,000 collaborators; they have received their response."
The 6,000 is an apparent reference to African Union peacekeepers in Somalia. Uganda contributes troops to the peacekeeping effort.
"We are behind the attack because we are at war with them," Al-Shabaab spokesman Ali Mohamoud Rage told reporters in Mogadishu, Somalia.
"We had given warning to the Ugandans to refrain from their involvement in our country. We spoke to the leaders and we spoke to the people and they never listened to us."
Rage said young suicide bombers carried out the attacks but did not specify their nationalities.
However, Police Chief Maj. Gen. Kale Kayihura told reporters arrests have been made in connection with the bombings. He would not say how many people have been arrested or provide details.
Suspicion had centered on Somali Islamist groups shortly after the explosions in Kampala. Islamic militants battling Somalia's U.N.-backed transitional government had previously threatened attacks on Uganda and Burundi.
A day of national mourning for victims of the bombings began Tuesday -- all flags on public buildings were ordered lowered to half-staff.
Eighty-five people were wounded in the Ugandan blasts, Kayihura said.
"This incident shows that it was terrorism," he said. Kayihura said he could not confirm that Al-Shabaab was responsible, but said the nature of the explosives used was consistent with the group's way of operating.
In addition to Ugandan victims, fatalities included one Irish citizen, one Indian, one American and 11 people who were either Ethiopian or Eritrean, according to the Ugandan government.
The blasts struck within 50 minutes of each other. The first one struck an Ethiopian restaurant in a neighborhood dotted with bars and popular among expatriates. Two others exploded at a rugby center.
The U.S. Embassy confirmed the death of the American. An organization that works with children in Uganda identified him as Nate Henn.
Crowley said Monday that the State Department has no reason to doubt Al-Shabaab's claim of responsibility, saying the "evidence so far at the attack scene would suggest an Al-Shabaab connection."