People Before Profit-Solidarity TD Paul Murphy has accused the Government of "standing by" while "thousands of tonnes of weaponry" pass through Irish airspace "to the Israeli military".
Mr Murphy accused Tánaiste Simon Harris of "studied, deliberate, false ignorance".
"Multiple airlines" are ferrying missile launchers, detonators and tear gas and other material, he told the Dáil.
"You're gas-lighting us about it," he accused Mr Harris.
Mr Murphy said he has a folder of waybills that document what the airlines are carrying, and claimed one of them had been sent to the Tánaiste ahead of shipment.
"You know about it. Why do you say you don't believe it is happening?" Mr Murphy asked the Tánaiste.
Mr Harris said that Ireland is seen "as almost an outlier - worryingly perhaps" in terms of support for international law and a two-state solution in the Middle East.
Mr Harris repeated remarks he made on RTÉ's The Late Late Show on Friday, saying that Ireland needs to have a better understanding of what is happening "in our skies and in our seas".
"I do think we need to do more on this," Mr Harris said, adding that work in the Department of Transport is ongoing.
"I do agree that any breach of Irish law must have consequences," he added.
Mr Murphy said the Government should prosecute the airlines carrying weapons and handed Mr Harris the folder containing the waybills.
Social Democrats deputy leader Cian O’Callaghan also asked why the Tánaiste had not investigated claims The Ditch website made about weapons being flown by airlines to Israel over Ireland.
Mr Harris said: "We do have clear laws about what can and can’t be flown over Irish airspace."
Mr O'Callaghan also raised the Israeli blockade on Gaza, which has entered its third month, and said the only thing Israel has sent in has been bombs and bullets
"Still the international community does nothing," Mr O’Callaghan said.
"We’ve seen nearly two years of relentless barbarism in Gaza … what is shocking though, is the continued silence of those in power.
"Tánaiste, on the Late Late Show on Friday, you said you don’t believe that weapons are being flown over airspace...on what basis?" he said.
Mr O’Callaghan said Mr Harris had not yet committed to passing the Occupied Territories Bill.
Mr Harris said nobody was dragging their feet.
He said, regardless of their political persuasion, "people are sickened, appalled and disgusted in relation to what Israel has done and are now proposing to do".
Mr Harris said he accepted that Ireland had to do more, but did not share the view of Mr O’Callaghan on what the European Union had done.
The Tánaiste said Ireland would continue to work at EU level to try to exert pressure on Israel.
"We are going to take forward legislation on the Occupied Palestinian Territories.
"But I will have to be honest in terms of passing legislation that is open to legal scrutiny," he added.
"I do hope in Ireland bringing forward legislation it might spur on other countries too," Mr Harris said.
Mr O’Callaghan said people in Gaza "needed action now".
