But the militant group said in a statement, without mentioning the government initiative, its mandate was "to liberate the Niger Delta people."
The government has also decided that the military presence in the region, which had been increased in the last few weeks, should be scaled down, a statement issued by the vice president's office said on Tuesday.
The southern Delta swamps, where many complain of poverty and oil spills, have been hit by militant attacks on oil and gas pipelines which have brought Nigeria's oil output to a 20-year low, and helped push oil prices to 2016 highs on Tuesday. [O/R]
President Muhammadu Buhari had appointed a team led by the national security adviser "to begin the process of a very intensive dialogue with those caught in the middle of this," Oil Minister Emmanuel Ibe Kachikwu said late on Monday.
"I want to call on the militants to sheath their weapons and embrace dialogue with government," he said. "We are making contacts with everybody who is involved, the ones that we can identify, through them, the ones that we can't identify so that there is a lot more inclusiveness in this dialogue."
"Probably we will suspend the operations of the military in the region for a week or two for individuals in the creeks to converge for the dialogue," he said.
Vice President Yemi Osinbajo, who had been expected to travel to London to meet investors on Tuesday, instead met Niger Delta state governors and military chiefs to discuss ways to end the militancy.
A statement from Osinbajo's office said it had been decided at the meeting that the military presence in the region should be "de-escalated," although forces would be kept to provide security for the talks.
Adding to the problems of authorities trying to stem the violence, a group in the southeast calling for secession declared support for the Avengers.
"We support the Niger Delta Avengers," said Uche Madu, a spokesman for the Movement for the Actualization of the Sovereign State of Biafra (Massob) which wants secession for the region which fought a civil war from 1967-70.
A former militant group, the Movement for the Emancipation of the Niger Delta, which laid down arms in 2009 under a government amnesty, accused the army of a "disproportionate use of force."
MEND, which was one of the largest militant groups, also said the Delta Avengers had attracted some of its former fighters. So far it has been unclear who is behind the Avengers.
There was no immediate direct response from the Avengers on the dialogue initiative. On its Twitter account it only issued a statement framing MEND leaders as criminals.
"Our struggle is focused on the liberation of the People of Niger Delta from decades of divisive rule and exclusion," it said.
Kachikwu also said Nigeria's oil output was between 1.5 million and 1.6 million barrels a day, down from 2.2 million barrels at the start of the year.
"Over the last two months, we have probably lost about 600,000 barrels from various attacks of militants in the area," he said.
Related story: Nigeria's new militants - The Niger Delta Avengers