Scottish police have begun talks with climate protesters from Greenpeace after its activists boarded an oil rig heading out to the North Sea.

Two protesters climbed on to the 27,000-tonne platform as it was being towed out of the Cromarty Firth, north of Inverness, after Greenpeace used boats to intercept it at about 6.30pm on Sunday.

The two activists unfurled a banner bearing the words “climate emergency” – a reference to the urgent need to reduce and halt fossil fuel use – after occupying a gantry on one leg of the rig underneath its main deck.

Greenpeace said the protesters had enough food for several days and were planning to remain on board until BP abandoned its new oilfields and switched to investing in renewables.

On Monday, Police Scotland liaison officers met Greenpeace support staff to try to negotiate a peaceful end to the occupation. As yet, no police officers are thought to have boarded the rig, but Greenpeace expects BP to quickly launch court proceedings in an effort to force the activists off the vessel.

BP refused to comment on its plans. The rig, Paul B Loyd Jr, is owned by Transocean and leased to BP for £140,000 a day. It was a Transocean rig operated by BP that caused the Deepwater Horizon disaster in the Gulf of Mexico.

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. Yet this rig, and the 30m barrels it seeks to drill, are a sure a sign that BP are committed to business as usual, fuelling a climate emergency that threatens millions of lives and the future of the living world.”

A Police Scotland spokesman said: “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.”

Nicola Sturgeon, the Scottish first minister, has adopted a tough target set by the UK Committee on Climate Change (CCC) to cut Scotland’s carbon emissions to net zero by 2045, but has not accepted demands to close down North Sea oilfields as a matter of urgency.

The UK government has not yet accepted the CCC’s net zero target of 2050 for the UK as a whole. The net zero concept allows some burning of fossil fuels, as long as the CO2 is captured and stored underground, or offset by tree planting or similar measures.

Describing the protesters’ actions as irresponsible for putting themselves and others at risk, BP said: “We share the protesters’ concerns about the climate. We support the Paris agreement. And we are working every day to advance the world’s transition to a low-carbon future.

“We’re reducing emissions from our own operations – down 1.7m tonnes last year – improving our products to help our customers reduce their emissions, and creating new low carbon businesses. We are committed to being part of the solution to the climate challenge facing all of us.”