Residents in Rangoon said Sunday the curfew is reduced from six hours to four hours a night. And Internet users say Web access was restored Saturday.
The government cut Internet service last month to stop the transmission of footage out of the country showing the military's violent response to mass anti-government demonstrations.
Human rights group Amnesty International says Burmese authorities detained at least four more prominent pro-democracy leaders Saturday.
U.S. Secretary of State Condoleezza Rice Sunday urged United Nations special envoy Ibrahim Gambari to return to Burma as soon as possible. Alluding to the detentions, she said Saturday's apparent unrest clearly demonstrates the need for an international presence in Burma.
Gambari Sunday begins a six-nation Asian tour aimed at increasing pressure on Burma's military government.
He met last month with Burma's top military leader, Than Shwe, and detained democracy leader Aung San Suu Kyi.
Gambari says he hopes to return to Burma after coordinating efforts with governments in Thailand, Malaysia, Indonesia, India, China and Japan.
Amnesty International says the government has rounded up thousands of activists and Buddhist monks since last month's crackdown. On Thursday, the U.N. Security Council issued a statement deploring Burma's pro-democracy crackdown, and calling for a genuine dialogue with Aung San Suu Kyi.
Burmese officials say the military action against the protesters left 10 people dead. But dissidents put the number of fatalities at 200.
Information for this report is provided by AP, AFP and Reuters