Australia sent additional troops after the attacks
Australian-led troops have begun hunting for rebel soldiers believed to be behind attacks on East Timor's two top leaders.
Soldiers backed by helicopters and armoured vehicles searched through jungle outside the capital, Dili, for suspects in Monday's twin shootings.
President Jose Ramos-Horta was shot three times, while PM Xanana Gusmao escaped unhurt from a separate attack.
Mr Ramos-Horta is in a serious but stable condition in a Darwin hospital.
A state of emergency remains in place in the country and security is very tight, with UN peacekeepers maintaining a heavy presence.
The UN force has been in East Timor since a wave of street violence in mid-2006.
A group of rebel soldiers with grievances dating back to that unrest are thought to have carried out Monday's attacks.
On Thursday, police were deployed to the home of rebel leader Alfredo Reinado, who was killed in the early-morning gun fight at Mr Ramos-Horta's residence.
Supporters have been mourning rebel leader Alfredo Reinado
Supporters crowded into his home after his body was brought there for burial.
Reinado, a former military officer, had been on the run with a group of followers since the unrest almost two years ago.
He was accused of being involved in several shooting incidents during the violence and charged with murder.
It is his armed followers that the Australian-led troops are now seeking out in the hills behind Dili.
Eighteen arrest warrants have been issued and more are being prepared, officials said.
On Friday, Australian Prime Minister Kevin Rudd is to visit East Timor to hold talks with Mr Gusmao.
Australia despatched additional troops to East Timor hours after Monday's attacks, in a bid to ensure stability in the fledgling nation.
East Timor gained independence in 2002, after decades under Indonesian rule.