A spokesman for the Movement for the Emancipation of the Niger Delta (Mend) said they would suspend attacks on oil installations for one month.
Newly sworn-in President Umaru Yar'Adua has said the crisis is a top priority and has called for a ceasefire.
Attacks in the Delta have led to a drop of more than 25 per cent in oil production. In its statement, Mend said it hoped President Yar'Adua would take advantage of its ceasefire "to ruminate on positive and realistic measures towards a just peace in the Delta".
Mend also said it had released six foreign oil workers kidnapped from a Chevron facility on the Pennington River on May 1. The Italian foreign ministry confirmed the release of the four Italians, one Croatian and one American and said they were officials from the US-based Chevron corporation.
In two separate incidents on Friday, 11 foreign oil workers and family members were kidnapped in southern Nigeria. It is not clear which group the gunmen were from.
Mend say they want local people to have more control of southern Nigeria's oil wealth. After his inauguration on Tuesday, President Yar'Adua announced he would hold a summit next week to seek a solution to the violence, but he postponed it on Saturday saying participants had asked for more time for consultations.
Mend's statement contained a warning to the president not to follow the example of his predecessor Olusegun Obasanjo.
"The present administration is treading the path taken by its predecessors in staging carnivals in Abuja and dialoguing with individuals... who [have] constantly been proven to be incapable of assisting in quelling the unrest in the Delta," the statement said.
Nigeria is Africa's top oil producer and fifth largest exporter of crude oil to the US. Although the bulk of the oil comes from the swamps of the Niger Delta, the region remains deeply impoverished, a reason often given by the militants for their attacks.
About 180 foreigners - most of them oil workers - have been kidnapped in the region in the past 18 months.
The hostages are usually released unharmed after ransom payments that both the government and the oil workers always deny.
Mend has communicated with the news media, including The-Latest, mainly using the internet.
- A Briton was one of four foreign oil workers kidnapped in Nigeria on Friday, the Foreign Office has confirmed. Local police say a group of gunmen, dressed in police uniforms, seized the employees in Port Harcourt.
The other kidnap victims were Dutch, Pakistani and another person whose nationality is not yet known.
More than 10 kidnappings of foreign oil workers in the past two weeks have been reported by local media, and more than 100 foreigners taken in six months. About 30 people are still being held for ransom in the Niger Delta area.
* See other articles on the subject in the 'World News' section of The-Latest.