WASHINGTON — The Trump administration’s top trade official warned Tuesday that Canada was running out of time to join the United States and Mexico in a new North American Free Trade Agreement, lamenting that the Canadians have proved unwilling to make “essential” concessions in significant areas of disagreement.

Robert Lighthizer, the U.S. trade representative, made the rare public comments about the state of the negotiations at an event in New York and insisted that the Trump administration will move forward with a bilateral trade pact with Mexico by Sept. 30 if an agreement cannot be reached with Canada. Such a move would anger the business world and face an uncertain path in Congress, which must ratify a final trade agreement.

“I think Canada wants to do it. I know we want to do it,” Lighthizer said at the Concordia annual summit. “We’ll see whether it happens. We’re sort of running out of time.”

In separate remarks Tuesday, Canada’s leaders demonstrated little urgency to close a deal this week.

Justin Trudeau, Canada’s prime minister, said that it was important that the United States and Canada find a win-win agreement.

“We know that Canada’s interests are what we have to stand up for and we will,” said Trudeau, speaking at the Council on Foreign Relations in New York. “We are looking for the right deal.”

Lighthizer and his Canadian counterpart, Chrystia Freeland, the foreign minister, agreed not to publicly share the details of their negotiations. However, Lighthizer acknowledged that protectionist barriers to Canada’s dairy industry and a disagreement over a mechanism for settling trade disputes between the two countries remain sticking points.

“The fact is that Canada is not making concessions in areas that we think are essential,” Lighthizer said.

Political considerations in all three countries are playing a role in the timeline to complete a revised NAFTA.

Despite Lighthizer’s threat to move ahead with just Mexico, he did not suggest breaking off trade relations with Canada if it fails to meet this month’s deadline.

The one promise that Lighthizer would make was that Trump would not let the new deal be called “NAFTA” — an agreement which he has derided for years as a failure.

“The president is not going to call it NAFTA,” he said. “We’ll call it something else.”