"If we're called on to contribute a stronger force in Somalia, we're ready to send an extra 2,000," spokesman Felix Kulayigye told Reuters by telephone.
The Al-Qaeda-linked al Shabaab group, which claimed the Kampala strikes, said it was avenging the killing of civilians by the African Union peacekeeping force. Ugandan forces form the backbone of the 6,100-strong deployment in Somalia.
Regional allies have promised to send an extra 2,000 soldiers to Somalia by mid-August.
Uganda's President Yoweri Museveni wants new rules of engagement that would allow the troops to take on the rebels in order to prevent further attacks across the region.
"We're in Somalia under the auspices of the AU to help our brothers there and al Shabaab won't intimidate us or scare us out of the country," Kulayigye said.
Burundi also has troops in Somalia's capital Mogadishu, shielding the presidential palace and guarding the airport and port from insurgents.
It has said it will not bow to pressure from al Shabaab and will keep its 2,500 peacekeepers in place.
