Witnesses reported that armed men and vehicles mounted with machine guns were stationed in opposition strongholds, while key roads in Mogadishu were blocked.
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"Both the Somali security forces and the pro-opposition fighters have taken positions along some key roads, there is civilian transport movement but, in some areas, they are not allowing anyone to move," witness Abdullahi Mire told AFP.
Somalia, recovering from decades of civil war, is facing its worst political crisis in recent years after the failure to hold planned elections in February.
President Mohamed Abdullahi Mohamed, best known by his nickname Farmajo, has faced harsh criticism at home and from foreign allies after signing a law earlier this month extending his mandate by two years.
On Sunday night, sporadic gunfire rang out across the capital after fighting broke out between government forces and those allied to various opposition leaders.
The clashes - mainly in the northern neighbourhoods of Sanca and Marinaya and the busy KM4 crossroads in the centre - began after dozens of opposition supporters marched in protest against Farmajo's term extension.
There were no immediate reports of casualties.
Tensions remained high on Monday, with some people trying to leave their homes in tense neighbourhoods.
"People are starting to flee from Bermudo area where the pro-opposition fighters have taken positions last night, the situation is tense and there can be an armed confrontation anytime if the situation remain the same," Fadumo Ali, a resident of one of the tense neighbourhoods told AFP.
"Some families have already left last night when the fighting broke out... we don't know how things will turn to be in the coming few hours but now it is calm and there is no fighting," said another resident, Feysal Hassan.
While schools and universities were closed, life in some of the unaffected neighbourhoods proceeded much as usual.
The crisis in Somalia has led to increasing dismay from the country's foreign backers, who have called on Farmajo to return to dialogue with leaders of the country's five federal states over the holding of elections.
"Highly concerned about the ongoing events in Mogadishu," European Union envoy Nicolas Berlanga said on Twitter Sunday.
"The general interest requests maximum restraint, preserve institutions that belong to all and dialogue. Violence is unacceptable. Those responsible will be held accountable."
Somalia's Prime Minister Mohamed Hussein Roble told a press conference Monday he was "disappointed with the violence aimed at destabilising peace and stability in Mogadishu during the holy month of Ramadan."
He urged security forces to "fulfill their national commitment and protect the stability of the people in Mogadishu."
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