Sinn Féin's Pearse Doherty claimed they have been "left in the dark" and raised suspicion that the government doesn't know what will happen either based on the "silence" from Education Minister Norma Foley so far.
He said many parents don't have confidence the government will get their kids back to school in a safe way.
Mr Doherty asked if all children will be back in school on a five-day basis in September.
Mr Varadkar acknowledged that hundreds of thousands of parents are concerned and more than a million children need to get back to school.
He said it's "crucial" schools are opened as planned provided coronavirus continues to be suppressed.
Mr Varadkar said the government want to get the decisions right and that confidence would be undermined if announcements were made and subsequently changed.
He said there are many other countries with higher instances of the virus than Ireland like Germany that have been able to reopen schools.
Mr Varadkar added: "There are other countries that have suffered much worse than us in this pandemic that never closed schools fully.
"I do think it would reflect very badly on us as politicians, on the government, and on the education partners if we were unable to open our schools in August."
Mr Doherty raised concern from some quarters that school uniforms would have to be banned as part of efforts to reduce the risk of the virus being spread.
Sinn Fein TD Pearse Doherty said they have been "left in the dark" (Brian Lawless/PA)
Mr Varadkar said interim public health advice has been published for schools and there is an emphasis on hand and respiratory hygiene.
He said no issues have been raised about the wearing of school uniforms.
Labour leader Alan Kelly said his two children asked him to find out when they will be returning to school.
He said Taoiseach Micheál Martin has said reopening the schools is the government's priority but added: "I'm not confident that's going to happen".
Mr Kelly said guidelines for third level institutions includes two metre social distancing and limits on class times.
He asked where this leaves the opening of schools suggesting teachers will want to be treated the same as third level staff
He claimed Ms Foley not answering a Dáil question on when the Leaving Certificate results would be released was a "disgrace" and demanded that she take Dáil questions on the reopening of schools in the coming days.
Mr Varadar said Ms Foley is scheduled to take questions in the Dáil next week.
He said that shops, restaurants and barbers are open, the Dáil is meeting, and many countries in Europe didn't close schools at all during the pandemic.
He said there's no reason why Ireland should be the only country that doesn't have schools reopening.