The DUP is demanding that Conor Murphy release all correspondence relating to a PPE joint order with Dublin that the Republic's Health Minister says was never placed.
The Sinn Fein Finance Minister told the Assembly in March that the joint consignment had been agreed with China. In April, he said the order had failed after "major economic powers entered the global race for PPE".
However, Simon Harris told the Dail on Thursday that he wasn't not aware of any joint order with Stormont being placed.
DUP MLA Paul Frew said: "Conor Murphy has it in his power to clear up the questions and end the confusion.
"He needs to now ensure that all emails, notes and minutes of discussions are published. Neither departmental officials or the minister should be deciding what they think is relevant or not.
"As deputy chair of the finance committee, an MLA and a citizen of Northern Ireland, I expect the Finance Minister to finally provide full openness and transparency."
Mr Frew said that the finance committee had requested all emails about the order but only some of the correspondence had been released and emails from March 30 and 31 were not provided.
He said that one explanation given was that these emails were judged irrelevant "because they related to the volumes, products, specification and pricing of PPE".
But he said that this made no sense as the bulk of emails released related to the same issues.
TUV leader Jim Allister said the claim of a joint PPE order had wrongly raised hopes within the NHS at a time when it was under tremendous pressure.
"There has been great reluctance to provide transparency on the issue," he said.
"Simon Harris' comments in the Dail this week, in which he confirmed that no joint order had existed between Dublin and Belfast, add to the need for urgent clarification on what exactly was going on."