Speaking by telephone a spokesman said: "We are now on hunger strike for however long - maybe for a few days, maybe for a month."
Police later confirmed the protesters had turned down the offer of food.
It is believed that up to 90 Kurds remain in the embassy, two having left early yesterday morning. They were taken into police custody.
Despite claims from police that negotiations were going well, there was still no sign of a breakthrough as the siege passed the 40-hour mark last night.
Diplomatic sources involved in the negotiations suggested things had taken a turn for the worse and that divisions may have arisen among the hostage-takers. Some wanted to give up and others wished to start a hunger strike.
Yesterday afternoon several of the protesters were seen on the roof of the embassy, holding bottles apparently containing petrol.
The day had begun with a flurry of pre-dawn activity, first with the arrival of the Labour peer, Lord Rea, a Kurdish sympathiser and member of the parliamentary human rights group. He met the hostage-takers. This was followed hours later by the decision of a man and a woman to leave the embassy. Both were taken into police custody.
At this point police and the protesters outside the embassy in Holland Park, west London, were talking of an imminent end to the stand-off.
Chief Superintendent Anthony Wills said: "We are relatively optimistic. There is no reason to be anything other.
"We are hopeful of a positive solution but we are prepared for the long game. The opinion of those in charge of the operation is that the patient game is the best option."
Chief Supt Wills said policewere also satisfied that the sole hostage, a Greek caretaker, Babis Pastsouris, was not in any danger.
The protesters' demands are not clear. While they have spoken of a desire to explain their situation, they have also requested a meeting with up to four unnamed MPs. They have also talked of a delegation to try to secure the safety of Abdullah Ocalan, but not given any details.
The legend of Mr Ocalan, the leader of the Kurdish Workers' Party (PKK) referred to by some Kurds as "Apo" or Uncle whose seizure by the Turkish authorities early on Tuesday sparked the storming of Greek embassies across Europe, has been the dominant factor at the protest. Protesters have erected a huge banner bearing his portrait while the crowd of up to 500 - regularly swelled by coachloads by Kurdish communities from around London - have been chanting his name.
"He is not the best chance for the Kurds, he is the only hope," said one 21-year-old man, wrapped in a red, green and yellow Kurdish flag, who asked not to be named. "He is the leader of the revolution. He is a hero. That is why we are here.
"The Turks think they can kill him. They think if they get rid of him they can get rid of 30 million Kurds, but they cannot. If they destroy him, we will just come together."
Another young man, who also asked not to be named, said: "These protests have not been organised. It is the reaction to Mr Ocalan being captured."
One woman, Isil Gulen, 29, said simply: "We believe that we need to be free. We have been fighting for 4,000 years. That is why we are on the streets."
Unlike on Tuesday when the atmosphere had been tense, the crowd yesterday remained in apparent good spirits as they sang and danced in a section of road close to the embassy that police had sealed off.
When news broke of the fatal shooting of three of their countrymen in Berlin, they held a minute's silence before again calling for Mr Ocalan to be released.
As the afternoon wore on, the veteran left-wing MP Tony Benn arrived to speak to the protesters through an interpreter.
Mr Benn said he had written to the Foreign Secretary, Robin Cook, demanding he immediately make clear Britain's position towards the Kurds. The Labour backbencher said: "History has shown time and time again that conflict of this character can only be resolved by political talks."Reuse content