It was not immediately clear if the attack on Tuesday was by the same group that is holding four foreign hostages and has staged a series of attacks on oil facilities in the world's eighth-largest exporter over the past month.
"There was a massive attack on the Agip offices in Port Harcourt," a government source said, asking not to be named.
Security sources said that eight of those killed were policemen and the other was a civilian.
The government source said that a group of about 30 men, armed with AK-47 assault rifles, arrived at the company's compound in two speedboats, engaged police in a lengthy shoot-out and robbed a bank within the premises.
An Agip spokesman in Nigeria confirmed the nine deaths and said it had "temporarily evacuated staff and contractors from the area of the base affected by the incident and the situation is currently under control".
In a separate development, Nigerian secret agents have detained two men suspected of helping fighters holding four foreign oil workers hostage, raising hopes of a breakthrough 13 days after the kidnappings.
Security sources said on Tuesday the men - officials in the southern Nigerian state of Delta - were picked up on Monday and were believed to have close links to Ijaw ethnic fighters whose month-long campaign of sabotage has cut a tenth of Nigeria's oil supply.