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."