According to The National, Kavo called for Duma to not mess up the Gulf LNG project "like he did" with the PNG LNG project.
Kavo asked Duma in Parliament why he "continued to insist" Shell would operate Gulf LNG.
Duma reportedly said he had no personal interest in the project and had not misled people.
The minister reportedly said InterOil had failed to contract a major player like ExxonMobil since signing the LNG project agreement with the government in 2009.
Gulf province has long suffered from a lack of services and infrastructure, while Kavo's comments relating to PNG LNG may have been a reference to Department of Petroleum and Energy involvement with landowner matters.
The Gulf LNG project is targeting 5 million tonnes per annum in 2014, with 3Mtpa from an onshore modular LNG plant and the rest from the floating LNG facility.
There is also a proposed ramp-up aiming to hit up to 8Mtpa from the total project through 2015 and 2016.
However, these plans do differ from the earlier strategy in 2009 which was based on an onshore 6-9Mtpa LNG plant adjacent to InterOil's oil refinery at Napa Napa.
Shell opened its Port Moresby office in Petromin Haus last month - an event Duma attended.
Shell and state-owned Gulf LNG project partner Petromin are working on a joint technical study agreement over the "major hydrocarbon basins in PNG", which is due for completion this year.