The British Prime Minister was speaking in the UK Parliament about Brexit negotiations
Article 50 of the Lisbon Treaty gives the right of a member state to withdraw from the EU.
Nominations to replace David Cameron will open on Wednesday June 29th and a new leader of the Conservative Party should be in place by September 2nd.
Speaking to the British Parliament earlier, Cameron promised to honour the result of the referendum result, even though it was not what he had supported.
He also reiterated that a vote to leave the EU did not mean turning Britain's back on Europe.
"There can be no doubt about the result ... I am clear, and the cabinet agreed this morning, that the decision must be accepted," Mr Cameron told parliament.
He said he had told German Chancellor Angela Merkel and French President Francois Hollande that more negotiations were needed before the UK will start the process of separating from the EU.
"The British government will not be triggering Article 50 at this stage ... this is our sovereign decision and it will be for Britain, and Britain alone, to take."
He continued: "Before we do we must determine the kind of relationship we want with EU.
"That is rightly something for the next Prime Minister and Cabinet to decide.
"I've also made this point to the Presidents of the European Council and the European Commission and I will make it clear again at the European council tomorrow."
Cameron spoke before Labour leader Jeremy Corbyn told MPs that the country is divided and will not thank either party for "indulging in internal factioning manoeuvring at this time".
Many of those who spoke in the parliamentary debate praised Mr Cameron for his work as Prime Minister and during the referendum campaign.
Corbyn said: "We thank him for his service ... As he announces the end of his premiership it is right to reflect that he led a government that delivered equal marriage ... I want to thank him too for his response to the bloody Sunday inquiry and how he reacted to the tragic murder of Jo Cox."
Additional reporting by IRN