Washington D.C. - Washington's new top diplomat, Secretary of State Rex Tillerson, met his Canadian and Mexican opposite numbers on Wednesday amid concerns over President Donald Trump's trade policy.

Canada, Mexico and the United States are members of the NAFTA free trade bloc, which Trump has branded a "catastrophe" for American jobs and has threatened to renegotiate.

The new US leader has also insisted that Mexico will pay for the anti-immigration wall he plans to build on America's southern frontier, possibly through an import tariff.

The continental neighbors are traditionally so close that summits between them have been dubbed the "Tres Amigos" in recent years. Maintaining strong ties will be a key task for the new U.S. Secretary of State.

But Mexico, in particular, has been offended by Trump's talk of paying for the wall, and Canada's Foreign Minister Chrystia Freeland has made it clear that Ottawa does not favor tariffs either. "Canada would respond appropriately," she warned at a news conference after her meeting in the State Department. "We do not know what the position of the United States will be when it comes to the notion of tariffs."

Mexican Foreign Minister Luis Videgaray has previously echoed the view of his president, Enrique Pena Nieto, that Mexico will never pay for the wall, describing the position as "non-negotiable."

A late evening State Department statement said Tillerson and Videgaray had a "constructive" conversation that touched on law enforcement, migration and security.

The pair "look forward to working together on the essential relationship between our two countries," it added, noting Tillerson is due to travel to Mexico City.

Videgaray's visit was not announced on the US secretary's public schedule and the pair did not allow reporters into their meeting, but he spoke briefly to Spanish-speaking reporters as he left. "It was a good first meeting," Videgaray said. "We agreed that we will have frequent meetings."

"Clearly, we are at a defining moment in the (bilateral) relationship," he added in an interview with Radio Formula. "And the Mexican government will continue to work with a positive and constructive attitude to reach good agreements, as long as it is in an atmosphere of respect for Mexicans."