Bosses - including those of BT, Marks & Spencer and Vodafone - signed a letter published in the Times, saying an EU exit would deter investment in the UK.
Leave campaigners point out two-thirds of FTSE 100 firms, including Tesco and Sainsbury, did not back the letter.
A referendum on whether the UK should stay in the EU will be held on 23 June.
David Cameron earlier took questions from employees of mobile phone giant O2, one of the signatories of the letter, at its headquarters in Slough, on the first of a series of tour events to sell his pro-EU message to voters. The move is designed to reach beyond Westminster and the emerging divisions within the Tory party.
The Mayor of London Boris Johnson, the most high-profile politician to back EU exit, has urged people to focus on the issues and played down talk of ill feeling between him and the PM, saying "team spirit" within the party was good.
In a move described by No 10 as "unprecedented", chairmen or chief executives of 36 FTSE 100 companies signed the letter, organised by Stronger in Europe and Downing Street, backing the campaign to stay in the EU, including Burberry, BAE Systems and EasyJet.
The FTSE bosses were among a total of 198 signatories from the business world, including the chief executives of Heathrow and Gatwick airports.
However, nearly two-thirds of the UK's largest publicly listed businesses did not sign, including RBS and Barclays.
Asked about why the majority of FTSE 100 companies did not sign the letter, Mr Cameron said companies were often reluctant to "make any form of political statement".
But he added: "If the leave campaign could produce 35 business leaders of this sort of stature they'd be over the moon and I don't think they have the prospect of doing that with FTSE 100 leaders in any way."
On Boris Johnson's decision to campaign against him, the prime minister said he had "huge respect" for the London Mayor and he had "great future in British politics" but added: "He has got it wrong on this one."
Bank of England governor Mark Carney, has meanwhile, said policymakers are "not making a judgment" on the outcome or consequences of the referendum.
Mr Carney told MPs on the Treasury Select Committee that the Bank was treating the June vote as it would "every other political event".
Analysis by the BBC's business editor Kamal Ahmed
For politicians supporting Britain remaining in the European Union, the blessing of business leaders is seen as a positive step.
And the list signing the pro-European letter - at least in part orchestrated by Number 10 - are certainly a hefty bunch. But a few health warnings.
First, many of the people who have signed have long been public advocates of Britain remaining in the EU. These include Sir Roger Carr of BAE, Iain Conn of Centrica, Dame Carolyn McCall of EasyJet and Bob Dudley of BP.
Second, some of the business leaders named say that although Britain would be better off economically in the EU, the UK is still a significant market.
Read Kamal's blog
The letter from business leaders said Mr Cameron had secured a commitment from the EU "to reduce the burden of regulation, deepen the single market and to sign-off crucial international trade deals".
The signatories wrote: "Business needs unrestricted access to the European market of 500 million people in order to continue to grow, invest and create jobs. Britain will be strong, safer and better off remaining a member of the EU."
John Holland-Kaye, the chief executive of Heathrow airport, denied he had been pressurised into signing the letter, saying his company wanted to get the message across that the EU had "opened up the aviation market and reduced the cost of flying".
"Lower costs of flying mean we can go on holiday more easily, we can go on business more easily - so whether you are going on a stag night or exporting there is a real benefit of being part of the EU," he told the BBC News Channel.
Richard Tice, co-founder of Leave.EU, said Downing Street had admitted using taxpayers' money and "applying pressure" on FTSE chairmen and chief executives to sign the letter.
"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," he said.
And Vote Leave, another group campaigning for EU exit said it was "disappointing to see the prime minister resorting so quickly to trying to scare people into voting for his deal".
A BT spokesman said: "Any suggestion that our company has been pressured into publicly supporting continued UK membership of a reformed EU is untrue" and it wanted to inform the public about how the EU benefits its business.
Find out where your MP stands
Meanwhile, senior figures from both sides of the debate are making their voices heard.
Boris Johnson urged people to ignore those "spreading alarm and anxiety" about the economic risks of EU exit, saying many of those involved supported the UK joining the euro in the 1990s.
"We have a great opportunity now to strike new deals for Britain to be the hub of new trading arrangements around the world," he said.
Former home secretary Alan Johnson, who is heading Labour's In campaign, has warned that two thirds of British jobs in manufacturing depend on demand from Europe and leaving could put up to 50,000 apprenticeships at risk.
"There is no progressive case for Britain to isolate itself," he said in a speech in Bristol. "We need to be leading in Europe, not leaving."
According to BBC research, 142 Tory MPs will campaign to remain in the EU, 120 to leave, while 68 have yet to make their positions clear.
Former Conservative leader Lord Hague has warned that splits over Europe in his party could take "generations to heal".
These divisions were laid bare during a debate in Parliament on Monday, when a succession of Tory MPs questioned the substance of the PM's agreement with EU leaders - announced on Friday.
The overwhelming majority of Labour MPs back continued EU membership as do the SNP, Plaid Cymru and the Liberal Democrats but the Democratic Unionists and UKIP are opposed.
Leaving the European Union would threaten jobs and put the UK's economy at risk, leaders of some of Britain's biggest companies have said.