Representatives of four rebel leaders - Ateke Tom, Soboma George, Farah Dagogo and Boy Loaf - told a news conference in Port Harcourt, the capital of Rivers state, that they wanted to meet Umaru Yar'Adua, the president, before signing up to the deal.
"Depending on the outcome of the said meeting, the leaders will then announce when they will begin to hand over the arms and ammunitions in their possession to the federal government," they said.
Education and rehabilitation
The four groups also called on the government to release Henry Okah, a suspected rebel leader, who is on trial for arms trafficking and treason.
Olusegun Adeniyi, a presidential spokesman, said Okah, who was arrested in Angola in September 2007 and extradited to Nigeria five months later, could be freed if he took the amnesty offer.
The region's main armed group, the Movement for the Emancipation of the Niger Delta (Mend), is not among the four that have welcomed the amnesty.
The formal amnesty programme is due to begin on August 6 to give the government time to set up 15 amnesty centres and train personnel for the disarmament, education and rehabilitation of the fighters.
"Between now and 6th of August, discussions are continuing with the leadership of the militants," Major-General Godwin Abbey, head of the government amnesty panel, said.
The government estimates that as many as 20,000 fighters and criminals could participate before the programme ends on October 4.
Attacks on oil facilities and government targets across the region, as well as a string of kidnappings, have seen crude oil production drop from 2.6 million barrels a day in 2006 to about 1.8 million.
Many of the armed groups argue that they are fighting for a greater share of oil revenue to remian in the Niger delta and complain of the pollution caused by the industry.