David Cameron said he hoped for a "reasonable, civilised" battle with eurosceptics as he renewed hostilities with Boris Johnson over the UK's future in the European Union.
The Prime Minister urged the public to choose "security, safety and certainty" by voting to remain in the EU in June's referendum - as he visited one of dozens of top businesses whose bosses backed his case in a letter.
He conceded that he was "quite conflicted" about the issue but that his time as Prime Minister had firmly persuaded him of the case - appearing to contrast his experience with that of the Mayor of London.
Mr Cameron said his close friend - who dramatically declared his support for the "leave" camp at the weekend - had a "very strong future in British politics" but repeatedly stressed his judgment was "wrong" on that count and he was "disappointed" by his stance.
"I just want people to know that I am speaking about this after thinking about it very, very deeply - after thinking about all the things I have learned as Prime Minister over the last six years," he told staff members at BT in Swindon.
"I have huge respect for Boris as a politician. He is a great friend of mine, he is a fantastic Mayor of London, I think he has a lot to give to the Conservative Party, I think he has a lot to give to this country.
"But on this issue I think he has got it wrong.
"We are going to have, I hope, a very reasonable, civilised argument between us and between other parties and you are going to find people with some fairly strange bedfellows. This is one where Jeremy Corbyn and I agree."
In the letter to the Times, chairmen or chief executives of 36 FTSE 100 companies said a Brexit would "deter investment and threaten jobs" - but the total number falls short of the 80 or 50 that it had previously been suggested would sign.
Car manufacturer Nissan, which employs 8,000 people in the UK, also added its voice to the campaign to remain, saying: "Our preference as a business is, of course, that the UK stays within Europe."
"Obviously we have got to listen to other voices as well," Mr Cameron said.
"But when we listen to businesses we are not just listening to what some big business chief might say, we are actually listening to the effect on jobs, to the effect on families' finances, to the effect on prosperity for our country and for all our people."
The PM said the referendum was more significant than a general election.
"I would argue this is a much bigger decision because at election times you can vote in a team of people and if you've got fed up with them after five years you can vote them out.
"This is a decision that lasts for life. We make this decision and it is probably going to be the only time in our generation when we make this decision."
In a direct appeal to wavering voters, he said: "We all feel quite conflicted. In all of us there is a questioning about 'what's the right answer for Britain'.
"I would say for anyone who is finding it hard to make up your mind, and you feel it is a very balanced decision, I would say come down on the side of security and safety and certainty."
Mr Cameron dismissed the idea a "leave" vote could lead to a second referendum on more favourable terms as a "complete illusion".
As well as BT, Asda, Marks & Spencer, Kingfisher and Vodafone chiefs backed the letter warning of the risks to the economy of quitting the 28-member bloc.
The letter includes some notable absences, such as Tesco, Sainsbury's and Barclays, but the chief executives of Heathrow and Gatwick have signed up.
The support from some of Britain's most well-known businesses will be welcomed in Downing Street as a growing number of Conservatives declared they would be backing the leave campaign.
But Mr Cameron was forced to defend using a Downing Street civil servant to lobby businesses to support the pro-EU campaign after MPs heard the letter was about to be published.
Leave.EU co-founder Richard Tice said: "We remember well how many large businesses and EU-funded groups like the CBI said we should join the euro. How wrong they were.
"The truth is that despite the bullying of a prime minister who has no real business experience, it is other normal commercial factors which will determine the continued success of British businesses to invest and grow."
A BT spokesman said: "Any suggestion that our company has been pressured into publicly supporting continued UK membership of a reformed EU is untrue."