The Shabab have been waging a relentless insurgency against Somalia's weak transitional federal government, and they have repeatedly threatened Uganda and Burundi for contributing troops to the African Union's effort to stabilize the country.

"We are sending a message to every country who is willing to send troops to Somalia that they will face attacks on their territory," Ali Mohamoud Rage, a Shabab spokesman, told reporters on Monday. He added, "Burundi will face similar attacks soon, if they don't withdraw."

The bombs exploded at 10:30 p.m. local time on Sunday here in Kampala, Uganda's capital, during the match between Spain and the Netherlands, striking a popular Ethiopian restaurant and a rugby field where large screens had drawn hundreds of spectators.

Visiting the bombing sites on Monday, President Yoweri Museveni of Uganda condemned the attackers as "backwards and cowardly."

"If they want to fight they should find soldiers, not attack people who are just enjoying themselves," Mr. Museveni said. "We shall look for them and get them, wherever they are."

Among the dead was at least one American, killed with scores of others at the rugby field. The aid group Invisible Children identified him as Nate Henn, saying he had raised money and advocated for child soldiers affected by years of warfare. Julie Cozzie, a neighbor in Raleigh, N.C., described Mr. Henn as a "kind, gentle, nice young man" who cared deeply for Uganda.

Officials said that, besides Ugandans, the dead included Indian, Irish, Ethiopian, Eritrean and Congolese citizens. The United States Embassy said it had offered to help in the investigation and warned of the possibility of more attacks.

The Shabab have long threatened to strike outside of Somalia and have carried out some smaller-scale, cross-border raids in Kenya. But Sunday's bombings greatly increased the group's reach beyond Somalia, and could ultimately recast some of the region's dynamics, particularly around security issues.

In a taped message broadcast last week on Somali radio stations, the Shabab's senior leader, Ahmed Abdi Godane, also known as Abu-Zubeyr, ordered militants "to wage revenge attacks against the Ugandan government for their killing of the Somali people."

Uganda, a close ally of the United States, was the first country to commit peacekeeping troops for the African Union's mission in Somalia, and without its military support the government would probably fall. Thousands of Somalis have also sought refuge in Uganda.

"This terrorist attack would really put pressure on the Somali refugees living in Uganda, their business and movement as well," said Ali Abdullahi Egal, chairman of the Fanole Human Rights and Development Organization. "It will also hinder the flow of refugees and asylum seekers who flee from their country and arrive in Kampala."

Somalia's president, Sheik Sharif Sheik Ahmed, vowed not to let the attack undermine the fight against the insurgency. Last week, East African heads of state agreed to send an additional 2,000 troops to Somalia, without specifying which countries would provide them.

"The international community and the region will not further tolerate the insecurity," he said.

Uganda is a predominantly Christian country, but the capital has a thriving Muslim community. Kale Kayihura, inspector general of the police, tried to assuage concerns that the bombing would make life harder for Somalis living in the country.

"Understandably, we must take extra security precautions," said Mr. Kayihura, citing an African Union summit meeting scheduled for late July in Kampala. "We are not going to target the Somali community as such, but the investigation will work closely with the community, the majority of whom we know are peaceful people."

Though close to many of Africa's most troubled regions, Uganda has remained relatively unscathed by the terrorism that has hit other parts of East Africa, notably in the bombings of American Embassies in Kenya and Tanzania in 1998, and attacks on Israelis on the Kenyan coast in 2002.

In the 1980s and 1990s, Uganda fought insurgents calling themselves the Lord's Resistance Army. In recent years, the group has degenerated into a band of several hundred living deep in the bush in Congo, Sudan and the Central African Republic.

The United States has provided the Ugandan Army with millions of dollars' worth of aid — including fuel, trucks, satellite phones, night-vision goggles and contracted air support — to hunt the fighters down.

Josh Kron reported from Kampala, Uganda, and Mohammed Ibrahim from Nairobi, Kenya.