Security officials told the BBC Monday they received reports of an explosion and 30 minutes of gunfire at the facility.
"The depot and loading tankers moored at the facility are currently on fire," the Movement for the Emancipation of the Niger Delta said in a statement.
In its statement, MEND said "heavily armed" men Sunday "carried out an unprecedented attack on the Atlas Cove Jetty in Lagos," the main entry point for ships entering Nigerian waters from the West and for oil tanker loading activities.
MEND's previous attacks have been in river and delta states south of Lagos. MEND officials said the group is fighting for a larger share of Nigeria's oil revenue to be retained locally.
Government leaders and MEND officials met Sunday to review last-minute details in the expected release of MEND leader Henry Okah, the Daily Independent newspaper in Lagos reported Monday. Officials said conditions for Okah's release and an out-of-court settlement of his treason charges were discussed.
Okah's lawyer, Femi Falana, said both sides would be in court Monday "and the proceedings will heavily depend on the outcome of the meeting."
President Umaru Yar'Adua, "is delighted to hear that Okah has accepted the amnesty offer, and commends the role played by his lawyer, Falana. He will be released when the formalities are concluded," an official told the Daily Independent.