Addressing a sombre House of Commons, Mrs May said she was "sorry" for the anxiety caused to the victims of the families by the way the Government responded to a Freedom of Information (FoI) request seeking the release of official papers.
She said all government documents - including cabinet minutes - had now been handed over to the independent panel set up by the former Labour government to review the papers for public release.
Once the panel had completed its work, all the documents would be made public, she said, with only "minimal redactions" covering details such as the names of junior officials and private information relating to the victims.
"As Home Secretary, I will do everything in my power to ensure that the families and the public get the truth," she said. "No government papers will be withheld from the panel, no attempts to suppress publication will be made, no stone will be left unturned.
"The principle underlying the process is that of maximum possible disclosure and disclosure to the families first and then to the wider public."
Ninety-six Liverpool football fans died in the crush as supporters tried to enter the Hillsborough stadium in Sheffield for an FA Cup semi-final on April 15, 1989.
Mrs May was responding in the first debate in the Commons chamber to be triggered as a result of an e-petition on the Downing Street website collecting more than 100,000 signatures.
The petition - calling for the release of all government-related papers concerning the disaster - was launched after the Cabinet Office turned down a request under the FoI Act for the documents to be made public. Mrs May acknowledged that the way the Government had handled the request had caused distress among the victims' families.
"The Government's position has absolutely nothing to do with attempting to suppress the release of these papers or to somehow hide the truth. And I am sorry that the way the Government responded to the FoI request caused anxiety among the families and concern on Merseyside and beyond," she said.
Source: PA