Tory MP Robert Syms says he and other Vote Leave Conservatives have told Mr Cameron he has a "duty" to stay on.
He wrote on Twitter that two-thirds of those who backed the Leave campaign had signed his letter.
While Mr Cameron headed up the Remain campaign, many of his MPs and some of his ministers backed the bid to Leave.
Counting is under way in the referendum that will decide whether the UK remains a member of the European Union but as yet, the result is seen as too close to call.
Mr Cameron, who has been prime minister since 2010 but has said he will not seek a third term, has vowed to stay on at Downing Street whatever the outcome.
But others, including former Conservative chancellor Ken Clarke, have suggested he will have to go if the Leave campaign win.
On Twitter, Mr Syms wrote: "This evening I delivered to Gavin Williamson MP, PPS to the prime minister a letter from Vote Leave supporters who are also Tory MPs.
"The letter thanked Prime Minister David Cameron for giving the British people a choice of their destiny today."
The letter says: "We believe whatever the British people decide you have both a mandate and a duty to continue leading the nation implementing our policies."
Mr Syms says it was "not possible to approach all Vote Leave colleagues to ask them to sign but many have expressed support" for David Cameron.
Among signatories listed by Mr Syms are former mayor of London Boris Johnson, former defence secretary Liam Fox, Zac Goldsmith, farming minister George Eustice and Andrea Leadsom, who represented the Leave side in some of the TV debates.
Eighty four Conservative MPs who campaigned for the UK to leave the EU have written to David Cameron urging him to remain PM, whatever the result.