In an interview with the ABC's Pacific Beat program on Monday, Kua said ExxonMobil had entered negotiations in bad faith, and the national share in the agreement was far lower than similar terms made for projects made in other countries.
"The entirety of the negotiations has been a farce," he said.
"Exxon came in to exploit our weak economic circumstances. How could we have ever struck a deal with that kind of mindset, that's not possible."
Despite the strong language, ExxonMobil could be granted the petroleum licence by the country's Petroleum Advisory Board.
But Kua said if the board rejects the application, all of ExxonMobil's residual interests would be extinguished, even suggesting it would lose its share in the licence and the government would look for other partners.
"The resource would be without a licensee and back to the drawing board for the state to open up conversations with any other interested parties," he said.
The integrated three-train expansion with PNG LNG, worth A$20 billion and set to double the nation's LNG exports, now faces questions if ExxonMobil can't develop a third train at its project. The two projects are being developed in tandem to avoid costly duplication.
The Total-led Papua LNG project reached a gas agreement last year to develop the Elk-Antelope fields to feed the two train expansion.
Oil Search has an interest in both projects, with Santos holding a share in the PNG LNG project and PRL3 where the P'nyang field is along with operator ExxonMobil.
Oil Search's outgoing manager Peter Botten suggested earlier this week the terms of the agreement put forward by the government were economically untenable.
"There is a need to balance out the fiscal regime that gives investors a fair return but returns to the state," he said.
"If you push the state take too high it doesn't appear an attractive investment for developers. There are boundaries you can't go beyond and still attract investors."
But Kua said on Monday the government was looking at existing agreements with countries in the region, such as Malaysia and Indonesia, saying the total take for PNG was far lower.
"Why is it that you are prepared to give a better deal to all other countries in Southeast Asia but not extend that to PNG," he said.
Botten has previously said it is impossible to compare them given the tremendous differences.
However just this week ExxonMobil has been accused of similar practices in the small South American country of Guyana by the human rights group Global Witness.
In a report released yesterday, the group said ExxonMobil had short-changed the nation US$55 billion dollars when it struck a deal in 2016 to develop the massive Stabroek field.
It said ExxonMobil used aggressive and rushed negotiation tactics when hashing out the deal with Guyana negotiators and the national interest in the license of 52% was far lower than the 65%-85% given to other countries in similar agreements.
Several reports made by Australia-based Jubilee Foundation over the years have said the economic and social benefits of the ExxonMobil's PNG LNG agreement, signed in 2014, were overstated and underdelivered.
Kua emphasised PNG was not the country it was 15 years ago and its refusal to accept what it saw as unfair terms "restored the dignity and pride of our sovereign nation."
"We're happy to wait -- a few weeks, months, years. If it happens it happens but it has to be on our terms, we are watching the world."
An ExxonMobil spokesperson told Energy News the company was disappointed it was unable to reach an agreement.
"We are hopeful that we can continue to work toward an outcome that benefits all stakeholders," the said.