Gusmao's move comes a day after he called on Mari Alkatiri, the prime minister, to resign and threatened to do so himself if Alkatiri refused to step down.
The president wants Alkatiri to take responsibility for the crisis that enveloped East Timor last month, when rival security forces battled on the streets and gangs rampaged, leading to more than 20 deaths.
It took the arrival of a 2,700-strong Australian-led peacekeeping mission several weeks ago to ease tensions.
Gusmao told crowds calling for Alkatiri's resignation outside the government headquarters in Dili that he had made a mistake.
"As your president, as your brother, I will honour the constitution... I will fulfil my obligations based on your demands," Gusmao told those gathered, prompting cheers of "Viva Xanana".
Sukehiro Hasegawa, the United Nations secretary-general's special representative to East Timor, also urged Gusmao not to resign, saying his continued presence was "indispensable for the maintenance of peace and stability".
Alkatiri, whose sacking of 600 security forces members sparked off the violence, has denied allegations that he armed a hit squad to kill his rivals.
He has refused to resign and appears to have the support of his ruling Fretilin party, which commands an easy majority in parliament.
Protesters demanded that Mari
Violence erupted in East Timor after Alkatiri in April fired nearly half the tiny nation's army, who had complained of discrimination because they came from the country's west.
Widespread violence and looting followed as sectarian tensions flared.
A UN administration ran East Timor after it voted for independence from Indonesia in 1999, until 2002.