The move follows an intensified offensive by Somalia's federal government against the rebel group over the past few months.
It has taken back control of several towns and villages in central Somalia with the help of US military, allied clan militias and forces belonging to Somali regional governments.
Kenya's President William Ruto, Djibouti's President Ismail Omer Guelleh and Ethiopia's Prime Minister Abiy Ahmed met their Somali counterpart Hassan Sheikh Mohamud in Mogadishu to review measures to weaken al-Shabab.
"The summit... agreed to jointly plan and organise a robust operational campaign at the frontline states level, of search and destroy on multiple frontlines aiming at key al-Shabab strongholds across south and central Somalia," they said in a joint statement.
"The time sensitive campaign will prevent any future infiltrating elements in the region," the communique said, without providing any details about the operation.
The three countries also contribute troops to the African Transition Mission in Somalia (ATMIS), an African-Union mandated peacekeeping force.
Al-Shabab did not respond to a request for comment.
The outfit has been fighting since 2006 to topple Somalia's central government and establish its own rule based on its strict interpretation of Sharia law.
It has launched significant attacks against hotels, military bases and government establishments in Somalia despite a relatively successful government push-back.
On Wednesday morning, mortars were fired in a district near President Hassan Sheikh Mohamud's office, where the meeting was held.
There were no reports of damage or casualties.
The militant group has also staged attacks in Kenya to pressure it into withdrawing its troops from ATMIS.Â
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