The authorities in East Timor have temporarily closed the international airport in Dili, after at least two people were shot dead nearby.
Mr Alkatiri stepped down after unrest earlier in the year
There have been ongoing clashes between rival gangs in the area in recent days.
The unrest began on Sunday, after the release of a UN report into factional violence earlier this year that left more than 30 people dead.
The report put much of the blame on the government of former Prime Minister Mari Alkatiri.
It concluded that former ministers, the police and the army had allowed weapons to fall into civilian hands, and said further investigations were needed to see if former Mr Alkatiri bore any criminal responsibility.
Mr Alkatiri stepped down as prime minister in June, under intense pressure both at home and abroad.
Battles among gangs of youths are common in East Timor.
At least one person died on Tuesday on a main road leading to the airport, and another person was reportedly shot dead in the area early on Wednesday.
The impoverished nation was rocked by two months of unrest earlier this year, triggered by Mr Alkatiri's decision to sack 600 disgruntled soldiers in March.
International peacekeepers had to be brought in to restore order, after thousands of people fled their homes as street battles broke out between rebel soldiers and those loyal to the government.