A Southern California-based aid group worker was among the dozens killed in the twin bombings in the Ugandan capital. An estimated 74 people died in the blasts.
In both explosions, people who were gathering to enjoy the World Cup final game were targeted.
The explosion sent soccer fans running for cover. The victims included an American, Nate Henn, who worked with an aid group based in San Diego. Police said Ethiopian, Indian and Congolese nationals were also among those killed and wounded, police said.
Fifteen people were killed in the first blast that went off about 20 minutes earlier at an Ethiopian restaurant.
Body parts found in the debris at the rugby club indicate that the attack was carried out by a suicide bomber.
The attacks raise concerns about the capabilities and motives of al-Shabab, which the U.S. State Department has declared a terrorist organization. If confirmed that the group carried out the attacks, it would be the first time al-Shabab has struck outside Somalia.
Officials suspect that the restaurant and rugby field were attacked because of the large number of foreigners present.
Several members of a church group from Pennsylvania were among the 60 people injured.
White House spokesman Tommy Vietor said the U.S. was prepared to provide any necessary assistance to the Ugandan government.
President Barack Obama was "deeply saddened by the loss of life resulting from these deplorable and cowardly attacks," Vietor said.
Officials said the Sunday attacks will not affect the African Union summit being held in Uganda from July 19-27. Many African leaders are expected to attend.
AP contributed to this report.