Mend, which has carried out attacks on oil pipelines and facilities, as well as kidnapped oil workers, declared a unilateral ceasefire on June 24.
The group said then that it was heeding calls by elders to give peace efforts another try.
Mend began fighting in 2006, demanding greater autonomy for the Niger Delta region and a larger share of the oil wealth it generates.
Brown said on Wednesday that Britain was ready to help Nigeria deal with unrest, which has cut Nigeria's output by a fifth and contributed to the rise in global oil prices.
Nigeria is the world's eighth biggest oil exporter.
Britain, Nigeria's colonial ruler until 1960, was ready to give help "to deal with the lawlessness" in the Niger delta, Brown said at the G8 summit in Japan.
He is due to meet Yar'Adua in London next week.
A spokesman for Brown's office said on Thursday that the prime minister had not committed to specifically offering military aid.
Britain is one of the largest investors in Nigeria. About 4,000 Britons live in the West African country, many working for large companies including oil and gas firms Royal Dutch Shell, British Gas and Centrica.
Yar'Adua has said that his administration will take a two-pronged approach to the unrest, pledging development for communities whose land and water has been polluted by oil extraction but also saying he will not tolerate the armed groups.
Goodluck Jonathan, Nigeria's vice-president, is organising a summit with armed groups, regional governors and oil companies to address the causes of the violence, although Mend has said it will not attend.
"We appeal to them to maintain the ceasefire so we can have a peaceful atmosphere for the summit," Ima Niboro, Jonathan's spokesman, said in response to the group's declaration.