"I do not think it would be right for me to try to be the captain that steers our country to its next destination," Cameron told reporters on Friday outside his Downing Street office.
Britain votes to leave EU in historic divorce
Cameron, who choked back tears, gave no detailed timetable but said there should be a new leader by the time his Conservative Party holds its annual conference in October.
"This is not a decision I've taken lightly but I do believe it is in the national interest to have a period of stability and then the new leadership required," he said.
Britain unleashes global turmoil as it votes to leave EU
"I think it's right that this new Prime Minister takes the decision about when to trigger article 50 and start the process of leaving the EU.”
Britain has voted to leave the European Union, results from Thursday’s landmark referendum showed, an outcome that sets the country on an uncertain path and deals the largest setback to European efforts to forge greater unity since World War Two.
Sterling plunges to 31-year low, biggest ever fall, as UK votes Brexit
British markets plunged on Friday, with sterling hitting a 31-year low in its biggest fall on record and UK stock futures pointing to a steep fall at the market open after Britons voted to leave the European Union.
WATCH: @David_Cameron resigns, confirms new Prime Minister will be in place for October.https://t.co/87gvhBQZb8
— Good Morning Britain (@GMB) June 24, 2016
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