Focus on Somalia
The summit comes two weeks after Somalia's al-Shabab fighters bombed Kampala in an attempt to force Uganda to withdraw its troops from their country and opened on Sunday with a solemn two-minute silence for the victims of the attack.
African leaders condemned al Shabaab and pledged to beef up an African force fighting the group that killed 76 people in Uganda this month.
"The African Union stands with you, my brother President [Museveni] and with the people of Uganda"
Bingu wa Mutharika,
African Union head
Jean Ping, the AU Commission chairman, called the al-Shabab attacks "despicable" and said the continental body was ready to step up its response.
"The commission is already planning the next phases in the deployment of Amisom in terms of the enlarged mandate, increased troop strength and appropriate equipment," he said.
Goodluck Jonathan, Nigeria's president, said his government condemned the attack and called al Shabaab "extremists".
Nigeria has pledged in the past to send troops to Somalia, but has yet to do so.
Earlier, Yoweri Museveni, the Ugandan president, urged African leaders to defeat "the terrorists" and "sweep them out of Africa" during his address.
Mutharika joined him in condemning the perpetrators of the Kampala blasts "in the strongest terms".
"The African Union stands with you, my brother President [Museveni] and with the people of Uganda," Mutharika said.
The bombings, at a rugby club and a restaurant, killed at least 74 people on July 11.
Al-Shabab said that the attacks were in response to the deaths of Somali civilians at the hands of AU peacekeepers.
The group, which the US says is allied to al-Qaeda, has warned of further violence in Uganda and Burundi unless they pull their troops out of Somalia.
Despite the attack, the AU said it is considering sending more troops to Somalia, which has topped the list of Foreign Policy magazine's "failed states"for the third year in a row.
Guinea and Djibouti announced a plan on Friday to send troopsto bolster the AU peacekeeping force charged with protecting the transitional government in Somalia.
If Guinea and Djibouti fulfil their pledges, it will provide a major boost to the 6,000 soldiers from Uganda and Burundi already deployed, although, in the past, larger African nations such as Nigeria and Ghana have not followed through on their promises of support.
Abdurahman Adnan Ibrahim, deputy prime minister of Somalia's transitional government, welcomed the troops and said the government was expecting more from the AU.
"The AU is now doing what we have been telling them for a long time that this [al-Shabab] is not only an enemy for Somalia but is the enemy of the whole region ... Every country now realises the reality on the ground," he told Al Jazeera.
AU diplomats has said that their peacekeepers' mandate would be reviewed at the Kampala summit and it was likely the 8,000-strong cap on troop numbers for the force would be lifted.
Al Jazeera's Andrew Simmons, reporting from Kampala, said that a more aggressive approach towards al-Shabab was likely to be adopted at the summit.
"There is definitely going to be an offensive message from this summit, definitely an increase in troops and possibly a change in mandate," he said.
"The question is whether this is going to bring Somalia back to some sort of peace after two decades of mayhem."
Al-Shabab, along with a number of other anti-government groups, controls much of southern and central Somalia, as well as most of the capital, Mogadishu.
The transitional government, which has long promised to launch a major offensive against al-Shabab, controls only a few streets of the capital.
"It's very difficult to fight the terrorists and win outright," Ugandan journalist Gawaya Tegulle said in an interview with Al Jazeera.
Tegulle said that President Museveni's aggressive remarks about al-Shabab "are a little misadvised."
"Confrontation against the terrorists will not work out, so maybe we need to adopt a different approach, maybe sit at the table with them and say, 'What do you want,'" he said.
At least 21,000 civilians are believed to have been killed in the violence over the past years, while 1.5 million have been forced to flee their homes.