The company issued a summons against the group yesterday and is seeking damages for losses following the "unlawful activities" of protesters during the week-long occupation of the Stena Dee oil rig off the Shetland Islands.
Greenpeace accused BP of trying to ruin it ahead of its application for a judicial review opposing further exploration in the Atlantic.
A spokesman for BP said: "We have begun proceedings against Greenpeace Ltd and other individuals in concern with unlawful activities on the rig and for the financial loss that we have suffered.
"Rigs of this kind are extremely expensive. It does not belong to BP but was on contract to the company and costs well in excess of pounds 100,000 a day. We have incurred a considerable loss and we would like to recover some of that money.
"It has nothing to do with the judicial review which is an entirely separate issue."
Those named in the summons, issued by the High Court in Edinburgh, are two senior directors of the group, Sarah Burton and Chris Rose, campaigner Liz Pratt and the captain of MV Greenpeace, John Castle.
Chris Rose said: "BP made pounds 1.5bn in its first six months of the year - it makes more in profit in 48 hours than Greenpeace receives income in a year. It is trying to use its financial and legal muscle to crush defence of the environment.
"BP may try to take away our money and our supporters' money, but ... it will not absolve them of responsibility for their role in global environmental pollution. BP is leading the world in the wrong direction by opening up fossil fuels that the climate cannot sustain. But it would rather close down Greenpeace than change direction and invest in solar power."
A "schedule of arrestment" was issued from the Edinburgh Court of Sessions, seeking pounds 1.4m from the group and the four members and "all moveable things in your hands belonging or obtaining to them". A hearing for an interim interdict is due to be held before the court today. The group's bank account has been frozen.
Greenpeace had begun landing activists on the rig on 9 August as it set out to begin testing work in the Foinaven field off the west coast of Scotland. The protest was part of a campaign to highlight alleged climate change. The last five protesters left the installation on Sunday after police moved in to evict them.
Four other campaigners were yesterday fined pounds 200 each for their part in the Stena Dee occupation. Patricia Fromm, 33, of Hamburg, Germany, Francis Hewetson, 32, from London, Ian Cameron, 29, from Guernsey, and Alexandra Hartridge, 23, from Hampshire, all pleaded guilty to a breach of the peace between 12 and 17 August. The four appeared at Aberdeen Sheriff Court handcuffed together and wearing bright orange boiler suits.
The application for judicial review is due to be heard by the High Court next month. Gerry Doyle, media director of Greenpeace, said the group had accused the Government of acting unlawfully by issuing licences for oil exploration in the Atlantic before carrying out an assessment of environmental impact. "The Government has failed to comply with an EU directive saying they should carry out the assessment before issuing licences for oil exploration. Greenpeace is saying the Government and 21 oil companies are acting illegally and if we are successful in our application it will delay oil exploration for a couple of years.
"We think this is why BP has issued this summons at this time. Normally they are very careful about their PR and how they are viewed by the public, but PR just flies out of the window when they can see that we might be successful in putting a stop to oil exploration in the Atlantic."
She said the group could be forced to lay off up to 70 of its staff in Britain if BP's lawsuit succeeded.