Mend leaders want the government to cater to a series of demands, including the withdrawal of the army from much of the region, before they can hand over their weapons.
But late on Sunday a government delegation told Mend that the deadline to hand over weapons would not be extended.
In June, Umaru Yar'Adua, the Nigerian president, offered amnesty to all gunmen in the Niger Delta to help check unrest which is preventing Nigeria from realising two-thirds of its oil capacity.
Disruptions of oil production have cost Africa's most populous nation billions of dollars in lost revenue.
As Mend made its announcement, a government delegation, which included Godwin Abbe, the defence minister, met two Mend senior members - Ateke Tom and Government Tompolo - at a rebel camp near Nigeria's oil hub Port Harcourt on Sunday.
Arms surrender rejected
Jonjon Oyeinfe, the former head of the Ijaw Youth Council ethnic rights group who attended the meeting, said: "Tompolo does not see justification for surrendering arms yet. Arms surrender was not supposed to be the first thing on the table. He wants the amnesty extended by three months."
Mend said on Monday the deadline could only be pushed back with the approval of Henry Okah, the group's suspected leader.
Okah in July agreed to take Yar'Adua's amnesty offer after charges of gun-running and treason against him were dropped and he was freed.
The unconditional pardon of Mend members is the most serious attempt yet by the government to resolve years of unrest.