An email to those who signed the petition said the prime minister and government had "been clear that this was a once-in-a-generation vote".
It said the decision "must be respected", and "we must now prepare for the process to exit the EU".
The UK voted to leave the EU by 52% to 48% in the referendum on 23 June.
Meanwhile, US President Barack Obama said he believed the UK would quit the European Union despite speculation the vote for Brexit could somehow be reversed.
"I think we have to assume that a referendum having been passed with a lot of attention, a lengthy campaign and relatively high participation rates is going to stick," he told a news conference at the end of a Nato summit in Warsaw.
The online petition gained more signatures than any other on the parliamentary website in the wake of the EU referendum result.
It had been set up by William Oliver Healey ahead of the referendum and had been signed by 22 people at the time of the result.
It states: "We the undersigned call upon HM Government to implement a rule that if the remain or leave vote is less than 60%, based on a turnout of less than 75%, there should be another referendum."
The referendum saw 17.4 million (51.9%) votes cast to leave the EU, compared with 16.1 million (48.1%) for remain, with a turnout of 72.2%, according to the Electoral Commission.
In its official response to signatories, the Foreign Office said the law which had set the rules for the referendum did not specify minimum conditions on turnout or margin of victory.
It added that the referendum was "one of the biggest democratic exercises in British history with over 33 million people having their say".
The email said the petition would be considered for a parliamentary debate by the Petitions Committee because it had received more than 100,000 signatures.
The committee is made up of 11 cross-party MPs and "almost always" debates petitions that reach 100,000 signatures.
It previously investigated the petition for fraud, removing 77,000 signatures which were found to be false.

The man, known as David, said he wanted answers about how Lincolnshire Police dealt with allegations against Gordon Dawson, a farmer from Spilsby.
Mr Dawson shot himself in 2007 after officers informed him of the inquiry.
In a statement, Lincolnshire Police said "procedures were correctly followed at the time" but policy has subsequently changed.
David claimed Mr Dawson had repeatedly abused him from the age of 15.
According to Lincolnshire Police, the first allegation was made in 1999 but no action was taken due to "insufficient evidence".
In 2006 police arrested Mr Dawson after four other men came forward claiming they were also abused as children between 1964 and 1986.
In early 2007 another alleged victim came forward.
An investigating officer phoned Mr Dawson on 23 March 2007 to tell him he would be questioned further and a few hours later he was found dead at his home.
Following Mr Dawson's death the investigation was dropped but David later complained to the police about the way the investigation was handled.
Speaking on the BBC's Victoria Derbyshire programme, David said: "We've had no justice, no finals, no process.
"It's been shutdown, shutdown all the way. I just want some answers."
Supt Rick Hatton said: "We have revisited the circumstances surrounding the investigation into Mr Dawson and are satisfied that the investigation that took place was thorough and robust, and no misconduct took place.
"However, a number of lessons were learned in relation to best practice and fed back to the Public Protection Unit.
"We are very sympathetic to the position of the victims in this case and appreciate they may feel that Mr Dawson was not brought to justice."
The force said any similar situation today "would see Mr Dawson's guns removed from him as policy is now quite different".
The government has rejected an online petition, signed by more than 4.1 million people, calling for a second EU referendum to be held.
[NEXT_CONCEPT]
Police have denied mishandling a sexual abuse investigation which left a victim claiming he had been denied justice.