Several Cabinet ministers have urged Scotland Yard to stop the demonstration.
Sir Mark was even summoned by No10 for talks with Rishi Sunak about the protest.
But after the discussions, it was clear that the Met boss had stuck to his guns in saying that there was no intelligence currently to show that the threat of public disorder was sufficiently serious to ban the march.
After the meeting, Mr Sunak stressed the force had agreed to keep the decision under “constant review”.
Mayor of London Sadiq Khan waded into the row shortly after the statement from No10.
He tweeted: “No one disputes that Remembrance events must be protected, but the policing of protests are operational decisions for the Met, not the Home Secretary.
“The government should be supporting the Met and our hard-working officers, not making their job more difficult.”
Mr Sunak said: “This weekend people around the UK will come together in quiet reflection to remember those who made the ultimate sacrifice for this country. It is not hyperbole to say that we are the beneficiaries of an inheritance born of their sacrifice.
“It is because that sacrifice is so immense, that Saturday’s planned protest is not just disrespectful but offends our heartfelt gratitude to the memory of those who gave so much so that we may live in freedom and peace today.
“But part of that freedom is the right to peacefully protest. And the test of that freedom is whether our commitment to it can survive the discomfort and frustration of those who seek to use it, even if we disagree with them. We will meet that test and remain true to our principles.”
He added: “This afternoon I asked the Metropolitan Police Commissioner, Sir Mark Rowley, to come to Downing Street and provide reassurances that the police are taking every step necessary to safeguard Remembrance services, provide reassurance to those who wish to pay their respects across the country and keep the public safe from disorder this weekend.
“It’s welcome that the police have confirmed that the march will be away from the Cenotaph and they will ensure that the timings do not conflict with any Remembrance events. There remains the risk of those who seek to divide society using this weekend as a platform to do so. That is what I discussed with the Metropolitan Police Commissioner in our meeting. The Commissioner has committed to keep the Met Police’s posture under constant review based on the latest intelligence about the nature of the protests.
“And finally, to our veterans and their families, I assure you that we will do everything it takes to protect this special weekend for you and our country, as we come together to reflect on those who protected our freedom.”