President Xanana Gusmao's closed-door meeting with the Council of State, an advisory board of 12 ministers, was expected to last all day and it was not clear whether they would agree on a replacement.
Alkatiri is also battling allegations that he armed a hit squad to silence political opponents, and an official in his office said Tuesday he had been summoned by Prosecutor-General Longuinhos Monteiro for questioning. The official asked not to be named, because he did not have authorization to speak to the press.
Many East Timorese say Alkatiri's dismissal of 600 disgruntled soldiers in March was to blame for street battles and gang warfare that left at least 30 people dead in the worst violence to hit East Timor since it voted for independence from Indonesia seven years ago.
Violence ebbed with the arrival of a 2,700-strong foreign peacekeeping mission and a U.N. team of experts landed in Dili on Monday to see what kind of support the world body could provide, including a promised long-term security presence, according to the AP.
One lawmaker urged the United Nations to take over the reins of power, as it did for two year's after East Timor's independence vote, saying the security forces needed to be reformed, democratic institutions rebuilt and confidence in the government restored.
Gusmao, who is revered throughout East Timor for leading its armed resistance to Indonesian rule, accepted the resignation effective immediately and began deliberations on the country's political future.
Russian MP and former boxer Nikolai Valuev responded to the insults that Ukrainian football fans made against Russian President Vladimir Putin during a Euro 2020 match.