Addressing mediapersons, Cameron said: "British people's will must be accepted. I fought this campiagn the only way I know going with what I strongly believe."
Announcing his resignation, Cameron said: "The country needs fresh leadership.I think we should have a new UK PM by October. I will do everything I can as PM to steady the ship over coming weeks and months. I will continue in post as Prime Minister with my Cabinet for the next three months."
Negotiation with EU will need to begin under a new PM, he added. "A negotiation with the European Union will need to begin under a new prime minister and I think it's right that this new prime minister takes the decision about when to trigger Article 50 and start the formal and legal process of leaving the EU," he said.
"British people made a decision that not only needs to be respected but those on losing side of argument should help to make it work. But I don't think it would be right for me to try to be the captain that steers our country to the next destination," Cameron added.
Cameron assured markets and investors that the British economy remained fundamentally strong after the nation voted to leave the European Union.
"I would reassure markets and investors that the economy is fundamentally strong," Cameron said in a televised statement outside Downing Street.
"I would reassure Britons living abroad and EU nationals here that there will be no immediate changes."
UK voted for the Leave campaign on Thursday making it clear that it would not be a part of the European Union. THe Leave campaign got 51.8 per cent of the votes polled whereas the Remain campaign got 48.1 per cent votes.
With PTI inputs