Taoiseach Leo Varadkar has rejected calls to sack Housing Minister Eoghan Murphy over the deepening homelessness crisis, claiming his cabinet colleague "did not cause the housing crisis".

Mr Varadkar defended Mr Murphy from growing criticism of his time in the job, despite admitting the latest record homelessness figures are "very depressing".

"I've full confidence in Eoghan Murphy as Housing Minister, it's a very difficult job.

"Eoghan Murphy did certainly not cause the housing crisis, that was caused by other people before this Government took up office," Mr Varadkar said after the Government's special cabinet meeting in Cork City.

"We shouldn't forget the record of other parties on housing, when this Government took up office eight or nine years ago the banks were bust, the construction industry collapsed, hundreds of thousands of people were in mortgage distress.

"That is the Fianna Fáil record and the opposition record when it comes to housing. Recovering from that was always going to be difficult, it was always going to take time," he said.

Asked to comment on the latest homelessness figures published on Tuesday - which show 10,305 people are in emergency accommodation, including 3,821 children - Mr Varadkar said the situation is "disappointing and very depressing".

However, he insisted his Government is doing what it can to address the crisis.

Not withstanding the disappointing and very depressing homelessness figures which showed a further increase, we are making progress in other areas, and while homelessness figures aren't going down the number of people we're lifting out of homelessness is actually going up as well.

"We're lifting more people out of homelessness than ever before, the difficulty is the number of people becoming homeless at a very fast rate," he said.