Mr Poots made the comments on the BBC's Nolan Live on Wednesday night.
Speaking to Sinn Féin's Alex Maskey, Mr Poots said: "We'll do business with you because it's in the interests of Northern Ireland.
"We have peace in Northern Ireland, so we'll hold our noses and do business with you."
He added: "I do not like doing business with Sinn Féin. I hold my nose about what has gone on in the past, about the activities of the IRA over 25 years, of the murders that took place and there's a stench that still rises from that in many homes across Northern Ireland."
Mr Maskey said the comments had shown Mr Poots in his "true colours"
However, speaking on the BBC's Good Morning Ulster on Thursday, Mr Poots said "many people across Northern Ireland find it appalling that Sinn Féin are in government".
"They have an association with the IRA, who committed over 2,000 murders in Northern Ireland, and that's something that's very hard for all of us to accept, but we do it because we want to ensure there aren't thousands more people lose their lives as the result of Troubles in Northern Ireland in the years to come," he said.
"Whenever I look across the benches at Stormont, I see people who have been charged and convicted and served lengthy prison sentences for the most heinous of crimes, and that is not the case for republicans.
"I work with those people because they have got a mandate, but that doesn't mean I have to like it."
Speaking on the Nolan Show, the DUP's Simon Hamilton said he "understood entirely" what Mr Poots had meant.
"I think my generation maybe didn't suffer as much as others did during the Troubles in Northern Ireland, but that doesn't mean that I don't forget what the IRA did," he said.
"But I have a family of my own now and I don't want them to grow up into the sort of Northern Ireland that many people had to live through in the 70s and 80s and because of that I'm prepared to work with, and my party is prepared to work with, Sinn Féin who have a mandate from the electorate.
"I know what Edwin meant when he talked about a stench and it is that legacy of violence, IRA violence, down through the 70s and 80s and into the 90s that left a lot of people dead, left a lot of people injured."
Mr Hamilton, the health minister, has come under criticism recently over the DUP's policy of keeping its ministers in office for only a few hours each week while talks continue to resolve the current Stormont crisis.
Asked about his position, he said he would resume his duties for one day next week.
The DUP's Edwin Poots has defended comments he made that party members have to hold their noses when doing business with Sinn Féin.