The meeting Somalia's capital has drawn leaders from three "brotherly neighboring countries."
President Mohamud posted pictures of the arrival of Kenya's William Ruto, Djibouti's Ismail Omar Guelleh and Ethiopian Prime Minister Abiy Ahmed.
They are there to discuss a coordinated military offensive against the Al-Qaeda linked group, which has been waging an insurgency in the troubled Horn of Africa nation for more than 15 years.
Security was beefed up in the city with movement restrictions, military patrols and all commercial flights were suspended.
"The major roads and streets in the city are closed today and there is no civilian movement allowed," Abdulahi Hassan, a member of the national security agency, said.
After taking office in May last year, Mohamud declared an "all-out war" on the jihadists, rallying Somalis to help flush out members of the jihadist group he described as "bedbugs".
In recent months, the army and local clan militias have retaken chunks of territory from the militants in an operation backed by US air strikes and an African Union force known as ATMIS.
But the jihadists who were forced out of the capital by African Union troops in 2011 have frequently retaliated against the latest offensive with bloody strikes.
The meeting comes a day after defense ministers and security chiefs of the four countries met in Mogadishu to prepare for the summit.
"This collaboration is expected to lead to the quick liberation of the country from the Kharijites (renegades) who have been dealt heavy blows on the battlefield in the past few weeks," the Somali government said on Tuesday, using a government term for Al-Shabab.
Although forced out of Mogadishu and other main urban centers, Al-Shabab remains entrenched in the countryside from where they have carried out numerous attacks both in Somalia and in neighboring countries.
In the deadliest Al-Shabab attack since the offensive was launched last year, 121 people were killed in two car bomb explosions at the education ministry in Mogadishu in October.
The group has also been active recently across the border in eastern Kenya, which is a contributor to ATMIS.
The 20,000-strong African Union force, formerly known as AMISOM, has a more offensive remit than its predecessor.
The force is drawn from Uganda, Burundi, Djibouti, Ethiopia and Kenya, with troops deployed in southern and central Somalia.
Its goal is to gradually reduce troop numbers to zero by the end of 2024 with security to be assumed by Somalia's army and police.
