Olivier Matthys AP/Press Association Images
Chief executive of the British Red Cross, Mike Adamson, made the comments last week following the deaths of two patients after long waits on trolleys in hospital corridors.
The charity said its staff and volunteers had been forced to step in to help transport hospital patients, due to a shortage of ambulances.
The prime minister today attacked the charity for what she called their "irresponsible" comments.
"He refers to the British Red Cross' term of a humanitarian crisis," May told Labour leader Jeremy Corbyn at Prime Minister's Questions in parliament.
"I have to say to him that we have all seen humanitarian crises around the world and to use that description of the National Health Service, which last year saw 2.5 million more people treated in A&E than six years ago, was irresponsible and overblown."
I have to say to him that we have all seen humanitarian crises around the world and to use that description of the National Health Service ... was irresponsible and overblown
Corbyn accused the government of trying to "fiddle the figures" on A&E waiting times in order to hide the scale of the crisis. He quoted warnings from the British Medical Association, the Royal College of Nursing that the health service faces a "dangerous" crisis of care as hospitals across the country struggle to meet demand.
The Labour leader also raised the case of a child who had been treated on two chairs pushed together in a corridor, due to a shortage of beds.
While May accepted that there had been "a small number of incidents where unacceptable practices have taken place," she did not accept that the NHS was facing anything beyond the normal winter pressures seen in the
"We acknowledge that there are pressures on the NHS. There are always extra pressures doing the winter," she said.
May also mocked the Labour leader for returning to the subject of the NHS after previously raising it in December.
"The right honourable gentleman asked me these questions before Christmas at the last PMQs. He may find it difficult to believe that someone will say the same thing they said a few weeks ago."
Corbyn responded by accusing the prime minister of being "in denial" about the crisis and mocked her claims earlier this week to be creating a new "shared society."
"The prime minister said she wanted to create a shared society. Well we've certainly got that. More people sharing hospital corridors on trolleys, more people sharing waiting areas at A&E departments, more people sharing in anxiety created by this government. Our NHS is in crisis but this prime minister is in denial," he said.