Workers on the majority of private sector contracts held by failed construction company Carillion will continue to be paid, the Insolvency Service said.
It announced that 90% of the company's private customers have indicated they want it to carry on providing services until new suppliers can be found and will provide funding to keep employees on.
The announcement came as a 48-hour period of support for firms working on Carillion's private sector contracts approached its end, with thousands of workers uncertain about their future.
The company's interim chief executive has revealed that Carillion had just £29 million in cash by the time it went bust, at a time when it was struggling under £900 million of debt and a £587 million pension deficit.
Labour leader Jeremy Corbyn accused the Government of being "deeply negligent", telling the House of Commons that the large salaries and bonuses paid to Carillion executives while the future of its 20,000 employees were put at risk showed there was "one rule for the super-rich, another for everybody else".
In fiery exchanges at Prime Minister's Questions, Mr Corbyn said the Government had a responsibility to ensure the construction giant, which held £1.7 billion worth of public sector contracts, was properly managed.
But Mrs May retorted: "We were a customer of Carillion, not the manager of Carillion, and that is a very important difference."
She revealed that Business Secretary Greg Clark was holding round-table meetings on Wednesday with affected banks, small businesses, trade bodies and unions.
And she welcomed agreements reached between Carillion's private sector service customers and the Official Receiver.
A spokesman for the Insolvency Service said that all of these companies had been contacted over the past 48 hours, adding: "Over 90% of these customers have indicated that they want Carillion to continue providing services in the interim until new suppliers can be found and will provide funding which enables the Official Receiver to retain the employees working on those contracts.
"Work has paused on construction sites, pending decisions as to how and if they will be restarted."