Sinn Fein TD Matt Carthy responded by calling the Fine Gael leader's comments "pathetic attempts at deflection" from his party's record in government.
After criticising the main opposition party at a Fine Gael event on Saturday, the Taoiseach rounded on opinion poll-leaders Sinn Fein again on Sunday.
Mr Varadkar questioned Sinn Fein's stance on legacy issues relating to The Troubles.
"It's highly disturbing, the idea of there being a Sinn Fein justice minister, or foreign affairs minister, or defence minister, is repugnant to me," he told RTE's The Week In Politics.
"There's a lot of people talking about some of the horrific things that are happening now in the Middle East. We have, in Sinn Fein, a party that will not acknowledge war crimes that may have happened in this country and they still need to be investigated.
"Those people need to be brought to justice and the families need to get the answers and justice that they need."
At a Fine Gael special conference on Saturday, Sinn Fein was criticised by Mr Varadkar and Minister for Higher Education Simon Harris in events with party members.
Justice and rural issues were addressed as Fine Gael gears up for the local council and European Parliament elections next June, with the threat of a general election also looming in 2024.
Sinn Fein's spokesperson on foreign affairs and defence Mr Carthy said that Fine Gael had overseen "abysmal records" while in power.
"In order to deflect from his party's failures in housing and health, Leo Varadkar has decided to shine a light on Fine Gael's equally disastrous legacy in justice and defence," he said in a statement to PA.
"After 12 years of Fine Gael government we have a retention and recruitment crisis within both An Garda Siochana and the Defence Forces. Morale with the Gardai is at an all-time low while communities feel less safe.
"Our Defence Forces are unable to fully provide the service they wish due to government underinvestment. Sinn Fein will turn around the abysmal records that Fine Gael have overseen.
"On foreign affairs, for decades Sinn Fein has developed important and long-standing international relationships with successive US administrations and on Capitol Hill. Coupled with our work in the EU, Australia and further afield, we are proud of our record in building support for the peace process and for Irish interests.
"We are also very proud of our record of international solidarity with South Africans in their struggle against apartheid, our track record on Palestine and supporting those who strive for peace and justice worldwide.
"On all of these issues we have worked constructively with government. Leo Varadkar knows this. His pathetic attempts at deflection will be seen by the Irish people for what they are."
Asked about whether the Irish Government had made a decision on taking a case against the UK Government over its legacy bill, Mr Varadkar said the decision would be made in the coming weeks.
The Northern Ireland Troubles (Legacy and Reconciliation) Act received royal assent despite widespread opposition from political parties, victims' organisations in Northern Ireland and the Irish Government.
Mr Varadkar said: "We're very much against the legacy legislation that the British government has brought through.
"We have a decision to make as to whether we bring an inter-state case against the UK Government or whether we support one of the third-party cases. We're going to make a decision on that in the next couple weeks.
"We have the advice from the AG (Attorney General), we haven't made a definitive decision yet, but we will make a decision on that in the next few weeks."