Jacob Rees-Mogg has been criticised for saying it would have been "common sense" to flee the Grenfell Tower fire, ignoring fire brigade advice.
The Leader of the House of Commons was appearing on a radio phone-in on the findings of a Grenfell inquiry report when he made the comments.
The Grenfell United group called the MP's comments "insulting". Mr Rees-Mogg said he "profoundly apologised".
Seventy-two people died in a fire at the tower block on 14 June 2017.
Speaking on LBC's Nick Ferrari Show on Monday, Mr Rees-Mogg said: "The more one's read over the weekend about the report and about the chances of people surviving, if you just ignore what you're told and leave you are so much safer.
"And I think if either of us were in a fire, whatever the fire brigade said, we would leave the burning building. It just seems the common sense thing to do.
"And it is such a tragedy that that didn't happen."
On Tuesday, Mr Rees-Mogg said: "What I meant to say is that I would have also listened to the fire brigade's advice to stay and wait at the time.
"However, with what we know now and with hindsight I wouldn't and I don't think anyone else would. I would hate to upset the people of Grenfell if I was unclear in my comments."
Grime artist Stormzy has called for Mr Rees-Mogg to resign. In a series of tweets, he said it was as if Mr Rees-Mogg was saying "those who lost their lives weren't smart enough to escape".
He wrote: "Let's bare [sic] in mind for 2 secs how horrifying and terrifying the situation would of been for the victims.... and then imagine they're being instructed by firefighters - trusted government authorities - to stay put."
In a statement, survivors' group Grenfell United said: "The Leader of the House of Commons suggesting that the 72 people who lost their lives at Grenfell lacked common sense is beyond disrespectful.
"It is extremely painful and insulting to bereaved families."
Replying to Mr Rees-Mogg's comments, Grenfell survivor Marcio Gomes said: "It's common sense not to build houses or flats with flammable material."
Hamid Al Jafari, who lost his father in the fire, said: "My dad had common sense but when they have no option what should they do?
"Saying sorry doesn't make any difference to us. Any MP needs to think about what they're going to say before they comment so they don't have to apologise."
Shadow Cabinet minister John Trickett said it was "not for a minister of the crown to second guess how those people would have reacted".
Tory MP Andrew Bridgen defended Mr Rees-Mogg's comments telling the BBC they were "uncharacteristically clumsy."
"Jacob is a leader, he's an authority figure.
"What he's actually saying is that he would have given a better decision than the authority figures who gave that advice."
Grenfell inquiry chairman Sir Martin Moore-Bick said fewer people would have died if the London Fire Brigade (LFB) had taken certain actions earlier.
Sir Martin criticised the LFB for following a "stay put" strategy, where firefighters and 999 operators told residents to stay in their flats for nearly two hours after the blaze broke out.
The advice is designed to prevent hundreds of people descending stairs while firefighters are coming up during a contained fire.
As flames spread around Grenfell's external cladding, the advice may have prevented some families escaping, the report found.
LFB Commissioner Dany Cotton told the London Assembly on Tuesday the brigade would respond differently to a Grenfell-like fire in the future.
She told the fire resilience and emergency planning committee: "Knowing what we know now about Grenfell Tower and similar buildings with ACM cladding, our response would be very different."