KAMPALA (Reuters) - Uganda said on Saturday it would mediate between Somalia and the breakaway region of Somaliland to facilitate reunification after a more than three-decade split.

President Yoweri Museveni of Uganda agreed to take up the role after a visit on Friday by a special envoy from Somaliland, Jama Musse Jama, according to a presidency statement.

"President Museveni agreed to be the unification facilitator between Somaliland and Somalia," it said.

Somaliland broke away from Somalia in 1991 but has not gained widespread international recognition for independence. It has been mostly peaceful while Somalia has undergone civil war.

"We don't support secession because strategically, it is wrong," Museveni was quoted in the statement as telling the envoy.

Reunification would potentially strengthen the Horn of African country's capability to tackle challenges including an insurgency by the Islamist group al Shabaab.

(Reporting by Elias Biryabarema; Editing by Andrew Cawthorne)