A Unites States based aid group says one of the dead is Raleigh native Nate "Oteka" Henn.
Henn worked for Invisible Children for a year and a half. The group helps children who've been recruited as soldiers in conflicts around the world - often against their will.
"Nate lived a life that demanded explanation. He sacrificed his comfort to live in the humble service of God and of a better world, and his is a life to be emulated," said Invisible Children in a statement.
The claim of responsibility by al-Shabab, whose fighters are trained by militant veterans of the conflicts in Afghanistan and Iraq, resets the security equation in East Africa and has broader implications worldwide. The group in the past has recruited Somali-Americans to carry out suicide bombings in Mogadishu.
Al-Shabab, an ultraconservative Islamic group that has drawn comparisons to the Taliban, has long threatened to attack outside of Somalia's borders, but the bombings late Sunday are the first time the group has done so.
"We warned Uganda not to deploy troops to Somalia; they ignored us," said Sheik Ali Mohamud Rage, al-Shabab's spokesman. "We warned them to stop massacring our people, and they ignored that. The explosions in Kampala were only a minor message to them. ... We will target them everywhere if Uganda does not withdraw from our land."
Rage said a second country with peacekeeping forces in Mogadishu
Burundi -- could soon face attacks. Fighting in Mogadishu between militants and Somali troops or African Union peacekeepers frequently kills civilians.
The attacks outside Somalia represent a dangerous new step in al-Shabab's increasingly militant path and raises questions about its future plans. The U.S. State Department has declared al-Shabab a terrorist organization. Other neighboring nations -- Kenya, Djibouti and Ethiopia, along with Burundi -- may also face new attacks, analysts say.
Despite the threats, the army spokesman for Uganda -- an overwhelmingly Christian nation -- said the county would not withdraw. "Al-Shabab is the reason why we should stay in Somalia. We have to pacify Somalia," said Lt. Col. Felix Kulaigye.
In Washington, President Barack Obama spoke with Ugandan President Yoweri Museveni on Monday to express his condolences for the loss of life in the bombings. Obama offered to provide any support or assistance needed in Uganda, said White House spokesman Robert Gibbs.
Gibbs said that, while the FBI is assisting in the ongoing investigation, the U.S. believes that there is "no clearer signal of the hateful motives of terrorists than was sent yesterday."
The death toll in Sunday's twin blasts rose to 74 on Monday, Ugandan officials said. Investigators combed through the blast sites, one an outdoor screening at a rugby club and the other an Ethiopian restaurant -- a nation despised by al-Shabab. Investigators found the severed head of what appeared to be a Somali suicide bomber.
In addition to Henn, officials said 60 Ugandans, nine Ethiopians or Eritreans, one Irish woman, and one Asian were also among those killed. Two people couldn't be identified. Eighty-five people were wounded.
At least three of the wounded were in a church group from Pennsylvania who went to an Ethiopian restaurant in Kampala early to get good seats for the game, said Lori Ssebulime, an American who married a Ugandan. Three Ugandans in the group were killed when a blast erupted. One of the wounded was 16-year-old American Emily Kerstetter.
"Emily was rolling around in a pool of blood screaming," said Ssebulime, who has helped bring in U.S. church groups since 2004. "Five minutes before it went off, Emily said she was going to cry so hard because she didn't want to leave. She wanted to stay the rest of the summer here."
Blood and pieces of flesh littered the floor among overturned chairs at the scenes of the blasts, which went off as people watched the game between Spain and the Netherlands.
"We were enjoying ourselves when a very noisy blast took place," said Andrew Oketa, one of the hospitalized survivors. "I fell down and became unconscious. When I regained, I realized that I was in a hospital bed with a deep wound on my head."
At a wrap-up news briefing Monday in South Africa, FIFA President Sepp Blatter denounced the violence against fans watching the game.
"Can you link it to the World Cup? I don't know. ... Whatever happened, linked or not linked, it is something that we all should condemn," he said.
Analysts have long feared that al-Shabab was turning increasingly violent. The International Crisis Group, an independent organization that works to prevent conflict, said in May that if foreign fighters' influence grew inside al-Shabab, the group's "rapid transformation into a wholly al-Qaida franchise might become irreversible. That could cause havoc even well beyond Somalia's borders, and the (Somali government) and the international community cannot choose to be bystanders."
Invisible Children, a San Diego, California-based aid group that helps child soldiers, identified the dead American as one of its workers, Nate Henn, who was killed on the rugby field. Henn, 25, was a native of Wilmington, Delaware.
"He sacrificed his comfort to live in the humble service of God and of a better world," the group said.
The FBI sent agents based at the U.S. Embassy in Nairobi, Kenya to assist in the investigation and look into the circumstances of the death of the American citizen, a State Department official in Washington said. The official spoke on condition of anonymity because he was not authorized to discuss the probe. Interpol said in a statement that it was dispatching a team to Uganda.
Ugandan President Museveni toured the blast sites Monday and said the terrorists behind the bombings should fight soldiers, not "people who are just enjoying themselves."
"We shall go for them wherever they are coming from," Museveni said. "We will look for them and get them as we always do."
Kulaigye, the Ugandan army spokesman, said it was too early to speculate about a military response to the attacks.
Uganda still plans to host the African Union summit in late July. More than 50 heads of state or government are expected to attend.
The U.N. Security Council condemned the attacks. Nigeria's U.N. Ambassador U. Joy Ogwu, the current council president, when asked whether the attack might deter African Union peacekeepers in Somalia, replied: "There is peace to be kept in Somalia and I don't believe that all member states, contributing states, will be daunted by such acts."
Ethiopia, which fought two wars with Somalia, is a longtime enemy of al-Shabab and other Somali militants who accuse their neighbor of meddling in Somali affairs. Ethiopia had troops in Somalia between December 2006 and January 2009 to back Somalia's fragile government against the Islamic insurgency.
Sunday's terrorist attacks are not the first to hit East Africa. U.S. Embassies in Nairobi, Kenya, and Dar es Salaam, Tanzania, were the targets of deadly twin bombings by al-Qaida in 1998, killing 224 people including 12 Americans. An Israeli airliner and hotel in Mombasa, Kenya, were targeted by terrorists in 2002.
The United States worries that Somalia could be a terrorist breeding ground, particularly since Osama bin Laden has declared his support for Islamic radicals there.