Greenpeace activists climbed on to the rig as it was being towed out to sea in Cromarty Firth, Inverness, on Sunday evening where they unveiled a banner declaring a "climate emergency".
The two Greenpeace protesters have now "set up camp" on the rig, the group said in a statement Monday.
Activities scaled a 27,000 tonne oil rig tonight in a bid to persuade BP to stop drilling new wells. BP says they care about climate change, yet they're pumping billions into the search for new oil while lobbying against tougher action on climate change.
Describing the protesters' actions as irresponsible for putting themselves and others at risk, BP said: "We share the protesters' concerns about the climate".
In a statement released by Greenpeace, an activist on the rig called Jo said: "Warm words flow from BP on their commitment to tackling climate change".
The rig - owned by Transocean and operated by BP - was making its way to the Vorlich field in the North Sea.
"The perverse idea we must maximise our oil and gas reserves can not continue". "That means the government must seriously reform the Oil and Gas Authority and instead invest heavily in the crucial work of helping oil communities like those in Scotland move from fossil fuels to the industries that will power our low carbon future".
Last month, Greenpeace activists blocked BP's London headquarters, demanding the company end its oil exploration.
"We're reducing emissions from our own operations - down 1.7 million tonnes previous year - improving our products to help our customers reduce their emissions, and creating new low carbon businesses".
BP said it was working with the rig owner Transocean and the authorities to try to resolve the situation.
The spokeswoman added: "We share the protesters' concerns about the climate". We support the Paris Agreement.
'We are committed to being part of the solution to the climate challenge facing all of us'.
A Police Scotland spokesperson told MailOnline: 'In relation to the ongoing protest involving Greenpeace in the Cromarty Firth, Police Scotland is working with the operators, the port authority and other interested parties in an effort to resolve the situation as safely as possible'.