Uganda's President Yoweri Museveni vowed to catch the perpetrators, and the UK's foreign secretary said he was "deeply shocked" by the bloodshed.
"I wish to condemn the
criminality of this day," Mr Museveni said, while visiting one
of the sites of the explosions.
"People who are watching football [soccer] are not people who should be targeted," he added. "If they [attackers] want a fight, they should go and look for soldiers.
"We should go for them because they are very irresponsible, backward and cowardly."
British Foreign Secretary William Hague sent his "heartfelt sympathies" to Mr Museveni and the families of those killed in the blasts.
"These were cowardly attacks during an event that was widely seen as a celebration of African unity, and I condemn them in the strongest possible terms," he said>
The UK will stand with Uganda in fighting such brutal acts of violence and terror."
At least one American national was among those killed by the bombs, which US President Barack Obama branded "deplorable and cowardly."
An AFP correspondent saw at least three wounded US citizens at Kampala's main Mulago hospital, where dozens were rushed in for treatment.
"We just wanted to watch the World Cup," said Chris Sledge, an 18-year-old US national who suffered serious injuries to his legs and a bruised eye, adding that he felt "OK" but was going to need surgery.
Fox News Radio said six Americans were injured - a figure backed up by Ugandan police Inspector General Kale Kayihura.
In a statement about the
attacks, U. Secretary of State Hillary Clinton said: "We
understand that American citizens may have been injured or
killed and our embassy is reaching out to assist.
"Our condolences go out to the families and friends of the victims, in the United States and Uganda."
The explosions hit an Ethiopian restaurant in Kabalagala, a crowded suburb in the south of Kampala littered with several pubs popular with football fans, and Kyadondo Rugby Club in the east of the capital - where Uganda's The New Vision newspaper was hosting a screening of the match.
Witnesses told The New Vision that two bombs exploded right in front of the giant screen relaying a live telecast from South Africa.
Police blamed Somalia's al Qaeda-inspired al Shebab militia as the death toll rose.
Al Shebab leader Mohamed Abdi Godane on July 5 accused the African Union (AU) peacekeepers - comprising Ugandan and Burundian troops - of killing civilians in Somalia's capital Mogadishu and called on Somalis to join the war against "the enemy of Allah."
"You know there have been declarations from al Shebab and al Qaeda. Terrorism is a modern-day threat. You know the region we are in and our commitment in Somalia," police chief Kayihura said/
"Obviously this is terrorism. That one is clear," he added. "At this stage we can't rule out anything."
Al Shebab did not immediately comment on the bombings. A website linked to the group carried a news story on the attacks, however, under the banner "glad tidings."
Despite the attacks, Uganda will not pull out its troops from Somalia, the country's Deputy Foreign Minister Okello Oryem said.
"These people are cowards and
Ugandans are not cowards, and we are not going to run away from
Mogadishu just because of this cowardly act," he said.