So far, only Royal Dutch Shell has admitted to being attacked by the group, which is holding four of Shell's foreign oil workers hostage.
But the group said on Wednesday it had now attacked platforms operated by Total and Agip - which both denied having been attacked - and said that it also intended to target Chevron.
The Movement for the Emancipation of the Niger Delta said in an email statement to Reuters: "The reports of attacks on Agip and Total flow stations are correct. We have decided not to limit our attacks to Shell oil as our ultimate aim is to prevent Nigeria from exporting oil.
"We will attack all oil companies including Chevron facilities."
The group began a wave of sabotage on the world's eighth-largest oil exporter a month ago, and Shell has shut 226,000 barrels a day, roughly 10% of Nigerian output.
"Pipelines, loading points, export tankers, tank farms, refined petroleum depots, landing strips and residences of employees of these companies can expect to be attacked. We know where they live, shop and where the children go to school," the group said.