Unconfirmed reports say one of the attackers, rebel soldier Alfredo Reinado, was killed as presidential guards returned fire.
Authorities have yet to confirm who led the pre-dawn attack.
One of the president's guards was also killed in the exchange of fire.
1975 - Former colonial power Portugal withdraws, Indonesia invades; two decades of resistance follow during which 200,000 Timorese are thought to have been killed
1991 - Indonesian troops fire on mourners at Dili's Santa Cruz cemetery, killing more than 100
1993 - Captured resistance leader Xanana Gusmao is jailed
1996 - Bishop Carlos Belo and resistance leader Jose Ramos-Horta share Nobel Peace Prize
1998 - Indonesia's president Suharto resigns; successor, BJ Habibie, suggests East Timor should be allowed to vote on its future
1999 - Massive turnout votes in favour of independence from Indonesia, triggering wave of violence from pro-Indonesian militia
2002 - East Timor declared independent with Gusmao as president
2006 - Clashes break out after 600 troops sacked from country's armed forces; Ramos-Horta appointed PM after predecessor, Mari Alkatiri, resigns
2007 - Ramos-Horta wins presidential election; Gusmao later appointed PM, prompting more gang violence
Meanwhile Xanana Gusmao, the country's prime minister, says he too escaped an ambush shortly after the attack on the president's home.
Speaking at a press briefing Gusmao said gunmen attacked his motorcade on Monday but no one was injured.
He said the attacks were part of a failed coup attempt.
Gusmao said the situation in the country "is proceeding normally and is under control" despite the attacks on the country's leaders.
"Even though the state has been attacked by an armed group and the president was wounded, the state is in control of stability," he added.
Following news of the attacks, the Australian government advised its citizens against travel to East Timor warning that the country could be thrown into instability with a risk of violence "anywhere at any time".
Kevin Rudd, the Australian prime minister, said he had agreed to a request from the East Timorese government for more Australian troops and police to be deployed to the country in order to maintain security in the wake of Monday's attacks.
"The request from East Timor is for a substantial and significant enhancement" of the some 800 Australian troops already in the troubled country on peacekeeping duties, Rudd told a news conference.
"For there to be a coordinated attempt to assassinate the democratically elected leadership of a close neighbour and friend of Australia is a deeply disturbing development," he said.
|Reinado was jailed for leading a mutiny |
in the army in 2006 [EPA]
Reinado, thought to have been behind Monday's attack, was wanted on murder charges over a flare up of violence in April and May 2006 that left 37 people dead.
The violence was caused by a split in the military that led to some 600 soldiers - about one-third of the defence force - being sacked.
Reinado was later jailed for leading a mutiny, but escaped from prison in September 2006 along with 50 others and has been on the run ever since.
In November last year Reinado threatened to use force against the government if it failed to concede to his demands.
East Timor was a Portuguese colony until 1975 and was then invaded by Indonesia, whose brutal rule over the territory led to the deaths of an estimated 200,000 people.
In 1999 a referendum was held on independence, triggering a wave of violence by pro-Indonesian militia.
An Australian-led peacekeeping force restored order and the country declared independence in 2002, but it has continued to be plagued by violence and gang fighting.