At least one American was among those killed in the explosions, which US President Barack Obama swiftly condemned as "cowardly".
The attacks came days ahead of the July 19-27 African Union summit in Kampala, which the government said would go ahead as planned.
"We have 64 dead and 65 injured. The nationalities of all the fatalities will be released later," national police spokeswoman Judith Nabakooba said.
Ugandan government spokesman Fred Opolot said police were trying to determine if suicide bombers carried out the attacks.
"While there is evidence to suggest that there were suicide bombers, at the same time it is thought that the bombs were under some chairs," he told reporters.
A US embassy spokeswoman confirmed one American was among the dead and an AFP correspondent saw at least three wounded US citizens at the city's main Mulago hospital, where dozens were rushed in for treatment.
"We just wanted to watch the World Cup. Unfortunately we went to the Ethiopian Village," said Chris Sledge, an 18-year-old US national who suffered serious injuries to his legs and a bruised eye.
"I feel OK. I'm going to need surgery," he said.
The attacks, which dampened the party mood around the first World Cup tournament held in Africa, drew a barrage of international condemnation.
France's Foreign Minister Bernard Kouchner described the attacks as "barbaric".
British Foreign Secretary William Hague said he was "deeply shocked" by news of the blasts, adding they were "cowardly attacks during an event that was widely seen as a celebration of African unity."
"The president is deeply saddened by the loss of life resulting from these deplorable and cowardly attacks, and sends his condolences to the people of Uganda and the loved ones of those who have been killed or injured,"