The march, according to organisers, would see demonstrators begin at Hyde Park in the capital before walking to the US Embassy and not walk past the Cenotaph war memorial in Whitehall.
Prime Minister Rishi Sunak said the Met Police had his “absolute and total backing” to tackle criminality.
Speaking to journalists in Dundee on Monday, Mr Yousaf was asked if he supported the march going ahead, saying: “Absolutely. I understand (the march) is taking place after the minute silence that we will all undoubtedly observe, I hear it’s not going anywhere near Whitehall or, indeed, the Cenotaph.
“And, of course, if Armistice was about anything, my goodness, it’s about peace.”
Marchers in Glasgow at the weekend
The First Minister added: “I am beyond angry at the Home Secretary and the UK Government who seem to want to drive every issue into a culture war.
“Describing those marches as hate marches is disgraceful, unacceptable.
“Yes, in every single march, I’m afraid you’ll get one or two idiots who will do and say something that we all universally condemn, but to describe those hundreds of thousands in London, in cities across the UK, including here in Scotland, as full of hate or hate marches is completely unacceptable.
“Frankly, this UK Government is unfit for office and certainly the Home Secretary is unfit for office.”
A spokeswoman for the Home Office said: “Remembrance Day is a time for national mourning and reflection, with the country united in paying tribute to those who paid the ultimate sacrifice for us.
“Peaceful protest is a cornerstone of our democracy, but the Home Secretary will always back the police to take action to prevent serious disruption and take a zero tolerance approach towards criminality.
“The Home Secretary has convened national policing leads and key government departments, as part of a wider exercise to ensure plans to tackle significant public disorder, at any event, are robust and effective.”
Over the weekend, the First Minister and his family were celebrating the return of his mother and father-in-law after almost a month trapped in Gaza.
Elizabeth and Maged El-Nakla were visiting his family in the region when the October 7 attack by Hamas sparked bombing raids.
But some of their extended family, including Mr Yousaf’s wife Nadia’s elderly grandmother, brother and his young children, remain in the region.
Speaking of their return, the First Minister said he and his wife had doubted if they would ever see them again.
“It’s bittersweet,” he said.
“I spoke to my father-in-law, in particular, it was the first time I ever saw him cry.
“He was really broken by the fact that he had to say goodbye to his mother, to his son, to their grandchildren, as well – the youngest of which is only three months old.”
He added: “As a family, of course, we’re happy and relieved to see my in-laws back, but it is, as I say, bittersweet because we are still in significant distress given the family that are still there but also the whole world is in distress at the scenes we are seeing unfold in Gaza.”
The First Minister went on to say that this was a “pivotal moment for the international community”, adding: “You either support the immediate ceasefire, as the Scottish Government has been calling for for many weeks, or you’re frankly enabling the suffering of innocent men, women and children, almost 10,000 of whom have lost their lives including over 4,000 children.
“I want Scotland to absolutely be on the right side of history, I hope that other countries will do likewise.”
The UK Government has been contacted for comment.