Five major Tamil separatist groups held to a cease-fire agreement today, but the government extended the state of emergency on this island nation for another month.

Officials of the government of President Junius R. Jayewardene said the routine continuation of the state of emergency, which has been extended on a month-to-month basis for two years, was approved by the cabinet in case of major violations of the cease-fire agreed to yesterday.

National Security Minister Lalith Athulathmudali said there were no violent incidents today between the Tamil minority, who make up about 12 percent of this country's 15 million people, and the majority Sinhalese.

The ethnic and religious civil war has continued for 10 years between the Tamils, who are mostly Hindu, and the Sinhalese, who are Buddhist, but the violence escalated during the past two months to almost daily attacks by one group or another.

The cease-fire was called to give Jayewardene time to work out a political settlement between the groups.

The more extreme Tamils have been calling for the creation of a separate state, known as Eelam, in the Northern and Eastern Provinces.

The government, however, appears to be trying to fashion some form of greater autonomy within the present system for those largely Tamil areas.

One private source here said he expects Jayewardene to gain between four and six weeks of "breathing space" with the cease-fire. But he raised the concern that the 78-year-old president will not move quickly enough to fashion a lasting solution.