Britons voted by 52% to 48%, or 17.4 million votes to 16.1 million, to leave the EU in a June 23 referendum, a result which most politicians have said should be respected but which some who voted "remain" are struggling to accept, Reuters wrote.
The petition called for the government to enact a rule that there should be another referendum if the vote for "remain" or "leave" was less than 60% based on a turnout of less than 75%.
The Foreign Office, the ministry that had steered through parliament the EU Referendum Act setting out the rules, responded that the legislation did not set a threshold for the result or for minimum turnout, according to the report.
"The Prime Minister and Government have been clear that this was a once in a generation vote and, as the Prime Minister has said, the decision must be respected," it said.
"We must now prepare for the process to exit the EU and the Government is committed to ensuring the best possible outcome for the British people in the negotiations."
Read alsoLegal steps seek to ensure UK Parliament votes on Article 50 - BBCBoth candidates to replace David Cameron as leader of the ruling Conservative Party and prime minister have said the result of the referendum should not be questioned and Brexit should be delivered, the report said.