However, Mr Bridgen has now used Twitter to say sorry following a huge backlash.
He wrote: “I realise that what I said was wrong and caused a great deal of distress and offence.
“It was not my intention to do so, and I do not want to add in any way to the pain that this tragic event has caused. I apologise unreservedly.”
I realise that what I said was wrong and caused a great deal of distress and offence. It was not my intention to do so, and I do not want to add in any way to the pain that this tragic event has caused. I apologise unreservedly.— Andrew Bridgen (@ABridgen) November 6, 2019
Mr Rees-Mogg told LBC on Monday that Grenfell victims should have used "common sense" and ignored fire service guidance to remain in the burning tower block.
Speaking to Radio 4 on Tuesday, Mr Bridgen said: "Jacob is a good friend of mine and he is an extremely intelligent and compassionate human being and his comments regarding Grenfell were uncharacteristically clumsy.
"But I think we have to put them into the context of Jacob."
Read more from Yahoo News UK:
When presenter Evan Davis asked Mr Bridgen if he believed Mr Rees-Mogg had meant to say “he would not have stayed put”, Mr Bridgen said: "That's what he meant to say.”
Mr Davis said: "That is exactly what people object to, which is, he is in effect saying, 'I wouldn't have died because I would be cleverer than the people who took the fire brigade's advice.’"
Mr Bridgen said: "But we want very clever people running the country, don't we, Evan? That is a by-product of what Jacob is, and that's why he is in a position of authority.
"What he is actually saying is, he would have made a better decision than the authority figures who gave that advice.”
Mr Bridgen’s apology follows Mr Rees-Mogg’s own apology for his comments.
Mr Rees-Mogg said: "I profoundly apologise. 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.”
Jacob Rees-Mogg should resign.— David Lammy (@DavidLammy) November 5, 2019
His suggestion that the 72 victims of the Grenfell Tower fire lacked “common sense” is unforgivable.
And his 'apology' is not an apology: it is just a cowardly attempt to pretend he said the exact opposite of what actually he said.
Tory MP Andrew Bridgen doubling down on Jacob Rees-Mogg’s horrific #Grenfell comments on #bbcpm.— David Lammy (@DavidLammy) November 5, 2019
He says "most people would probably defer to the advice of an authority figure" but “Jacob is a leader ... (who) would have made a better decision".
Gross superiority. Unforgivable.
Reacting to Mr Rees-Mogg's apology, the Fire Brigades Union said Grenfell residents had been in a "terrifying, impossible" situation, and added: "It was... callously irresponsible for a senior government figure to suggest that the public should ignore firefighters when they are in a fire."
Andrew Gwynne, Labour's national campaign co-ordinator, said Mr Bridgen's comments were "contemptible" and that he should be removed as a parliamentary candidate.
Labour MP David Lammy said in a tweet that Mr Bridgen's comments were “unforgivable” and demanded his resignation.