Mr Varadkar told the Dáil on Wednesday this would be a “more significant statement” and said the EU had been “far too passive” on the issues of the two-state solution and Palestinian statehood.
Ms Bacik also called for the enactment of the Occupied Territories Bill, which seeks to prevent Ireland from trading in goods and services imported from Israeli-occupied territories.
In response, the Fine Gael leader said the advice of a number of attorneys general was that the Bill could not be enacted by the Dáil because trade is an EU competence.
“That’s been the view now for three or four attorneys general from all sorts of different backgrounds in the last previous Governments,” Mr Varadkar said.
He added that the Government favoured the recognition of the state of Palestine, and the Dáil and Seanad had passed motions to that effect.
“We don’t believe that the best way to do it is unilaterally. That will be dismissed. It will be ineffectual, and we will be seen as an outlier, acting unilaterally, at a European level,” Mr Varadkar said.
“What we would like to do, is do it as part of a group of European countries. I think that will be a more significant statement. We don’t just want it to be a statement, we want it to be part perhaps of an agreement to end the violence that’s happening at the moment and to put in place a new administration in Gaza for the day after.
“And that’s the kind of conversation that we’re having at the moment, for example with Spain, which has a similar view to ours, and some other countries as well.”
Mr Varadkar said he would be pressing at EU Council level next week for a text that will call for a permanent ceasefire and for the EU to take a more active role in pushing for a two-state solution and Palestinian statehood.
“The European Union has been far too passive for far too long when it comes to this topic,” he said.
Ms Bacik said the Government could do more and TDs were continuing to receive thousands of emails from people across the country who want the Coalition to “do more, who are urging a stronger stance at international level from you in Government and indeed here in Ireland too”.
“We want to see a stronger response from Ireland pushing at EU level to ensure that other EU member states can be brought on board to seek that crucial goal of a permanent humanitarian ceasefire,” she said.