The parties discussed the path towards reopening the mine, operated by Barrick Nuigini (BNL), which was mothballed in April after PNG refused to extend a special mining lease (SML).
The negotiations are yet to be finalised, both parties noted on the weekend, with tax concessions a possible sticking point.
BNL is challenging both the SML refusal and PNG's decision to award an SML to state-owned Kumul Minerals Holdings in August; and has separately sought a resolution through the World Bank's International Centre for Settlement of Investment Disputes.
Bristow flew to Port Moresby last week to discuss the terms of reopening the mine with prime minister James Marape and Enga provincial governor Sir Peter Ipatas.
"We have agreed in principle that Papua New Guinea will take a major share of equity under the new arrangements and BNL will retain operatorship and there will be a fair sharing of the economic benefits," Marape said in a joint statement following Thursday's meeting.
"I am certain that my team will be able to work with the PNG state negotiation team, led by SNT Chairman Ambassador Isaac Lupari, in finalising full commercial details," Bristow said.
Both parties then issued separate comments over the weekend.
Marape said on Facebook he appreciated Bristow and his team "who came to negotiate hard for their company but also responded well to all our core issues I could not compromise".
He said "subject to final touch ups" he had not compromised on principles including the SML remaining under Kumul, PNG would make no concessions on taxes, all outstanding legacies were not conceded and Barrick was "to phase out at an agreed time".
However, BNL said on Saturday its position was that "all economic levers, including taxes, must be open to consideration to achieve a fair and equitable split of economic benefits".
It also maintained that SML 1 was the appropriate tenement because it possessed the 14 associated tenements for the mine to operate, a mining development contract and other permits, while SML 11 purportedly granted to Kumul had none of the above approvals, which could take years to obtain, and was "having its legitimacy challenged in the PNG courts by both BNL and landowners".
It also said the two sides had agreed any legacy issues would be limited to transgressions against law, contract or permit and disputes would be resolved under historical agreements.
Porgera is owned 47.5% by both Barrick and Zijin Mining, and 5% by the Enga provincial government and landowners.
Before withdrawing guidance, Barrick had expected its share of Porgera production to be between 240,000-270,000 ounces of gold this year.
The mine had "tier one potential but faces many challenges in the form of legacy issues and an unruly neighbourhood," Bristow had said in Barrick's 10-year production plan released earlier this year.