Talks on the TPP, ditched by US President Donald Trump in one of his first acts in office, have been held on the sidelines of Asia Pacific Economic Cooperation (APEC) meetings in the Vietnamese resort of Da Nang.
Clear agreement on proceeding without the US would be a boost for the principle of multilateral free trade pacts over the bilateral deal-making that Trump favors.
But while Japan has been lobbying hard for a quick agreement to move ahead, Canada, New Zealand and Malaysia are among countries that have appeared less enthusiastic to hurry.
"We have collectively reached the stage where we can discuss a proposal for a final package for an agreement in principle of the TPP," Japanese Economy Minister Toshimitsu Motegi said.
"I would like to emphasize once again the importance of reaching an agreement in principle right here."
Motegi said negotiators had tried to reach a conclusion satisfactory to all, "or put in a different way, a conclusion that makes everybody equally unhappy."
The TPP aims to eliminate tariffs on industrial and farm products across a bloc whose trade totaled $356 billion last year. It also has provisions for protecting everything from labor rights to the environment to intellectual property - one of the main sticking points.
As ministers left the first meeting on Thursday, they said more discussions were needed. An official said they were expected to meet again in the evening ahead of talks between TPP leaders on Friday.
"We've got more work to do, but we are inching closer to an agreement so I remain very hopeful," Australian Trade Minister Steven Ciobo told reporters. Mexican Economy Minister Ildefonso Guajardo said talks were "very productive." Vietnam said some new issues had cropped up that needed further discussion.
Among options being discussed by TPP countries is whether to suspend some provisions of the original agreement to avoid having to renegotiate it and potentially to entice the US back in the long term, officials said.