10 March 2016 Last updated at 09:48 GMT
Describing the current conditions of the camp as "atrocious", the minister said the area was never meant to be a migrant camp.
"We must insist that these people are treated humanely, and then find a way out to Europe because they don't want to stay in Greece."
Mr Katrougalos explained it was a legal obligation for other states to take migrants under last year's EU relocation plan.
On Wednesday, Macedonia announced it would not let any migrants through its border with Greece, effectively blocking the Balkan route north.
The decision came after Slovenia barred access to migrants transiting the country. Serbia and Croatia have said they would follow suit.
Some 13,000 migrants are now stranded at the Macedonia-Greece border.
Watch the full interview on BBC World News and the BBC News Channel on Thursday 10 March 2016. The interview is also available on BBC iPlayer (UK only)
Greece will try to ensure that conditions at the country's Idomeni migrant camp are "humanely acceptable", the Labour and Social Security minister George Katrougalos has told BBC HARDtalk's Stephen Sackur.