AUGUSTA — The governors of Georgia and South Carolina met privately and far from their statehouse offices Friday to discuss disagreements that have left years of cooperation toward building a shared seaport on the Savannah River in limbo. They left without saying if they were any closer to a resolution.

Georgia Gov. Nathan Deal and South Carolina Gov. Nikki Haley met for almost two hours at a private office building in downtown Augusta before they were whisked away without pausing to speak with reporters outside.

“It was a productive meeting and the two governors will continue to work together on projects that bring jobs to both states and benefit the entire Southeast,” Deal’s spokesman, Brian Robinson, wrote in an emailed statement. He declined to be more specific.

The neighboring states operate competing container ports in Savannah and Charleston. Since 2007, they have also worked together on developing a $5 billion shipping terminal in Jasper County, S.C., across the river from Savannah. The states would share the new port 50-50 and have already spent more than $3.6 million apiece.

Progress on the Jasper terminal broke down altogether in December when South Carolina port officials voted to stop funding the project. Bill Stern, board chairman of the South Carolina State Ports Authority, said Georgia needed to make some concessions before his state would spend another dime.

South Carolina officials say they fear the Savannah River won’t be deep or wide enough to handle newer, supersize cargo ships even if Georgia meets its goal of dredging the 32-mile shipping channel from 42 to 48 feet deep. They want Georgia to commit to seeking a depth of 50 feet and to study whether the river can handle traffic for both the Savannah port and the proposed Jasper terminal.

Stern attended the governors’ meeting Friday along with South Carolina ports CEO Jim Newsome. Both declined to comment on what was said inside, but Stern said his positions had not changed.

“Let’s see if this is a viable port or not, which means 50 feet and two-way traffic,” Stern said. “Let’s be good stewards and stop spending public money until we know we can build something.”

Georgia Ports Authority chief Curtis Foltz and state port board Chairman Alec Poitevent also joined Deal for the meeting. Neither would comment afterward, referring all questions to the governors. In the past, both men have said they’re committed to building the Jasper County port

Foltz has said previously he’s certain the Savannah River could accommodate two ports once it’s deepened to 48 feet. The giant cargo ships are already using Savannah’s port, though the river remains too shallow for them to navigate at low tide.

Stern said port officials from both states agreed to a future meeting on the Jasper terminal, though no date has been set. Deal’s spokesman confirmed both sides would meet again.

The latest negotiations on the proposed Jasper County port came soon after South Carolina state lawmakers took their strongest steps yet to stop Georgia from deepening the river to benefit the Port of Savannah. Both chambers of the state Legislature have voted unanimously to invalidate a water quality permit granted for the project last year by South Carolina’s environmental agency.

That legislative measure is expected to be vetoed by Haley, who worked with Deal to urge her state’s regulators to compromise with Georgia after the permit was initially denied. That outraged legislators who saw Haley giving an advantage to one of its major shipping rivals.

Both states are scrambling to deepen their harbors at Savannah and Charleston to accommodate supersize ships expected after the Panama Canal finishes a major expansion in 2014. Georgia port officials hope to finish their dredging in 2016. South Carolina officials say their earliest target for completion is 2020.