President Trump's economic and immigration policies are not undermining the United States ability to advance other policy goals with Mexico, according to Secretary of State Rex Tillerson.

"There is an understanding that there is much more to the U.S.-Mexico relationship than just NAFTA," Tillerson told reporters Thursday. "The wall does not define our relationship."

Tillerson, along with Homeland Security Secretary John Kelly, hosted their Mexican counterparts at the State Department for a discussion about how to counteract drug trafficking into the United States.

But President Trump's team has notified Congress of his desire for fast-track authority to renegotiate NAFTA, which raised questions during the press briefing about whether the notification jaundiced the drug trafficking discussion. Tillerson emphasized that cooperation would continue throughout the economic talks.

"We had... very open, very frank, very candid conversations about where we have succeeded in the past, what is standing in the way of our success in the future," he said. "[And] a very strong commitment to overcoming whatever those obstacles may have been in the past."

Mexican Foreign Minister Luis Videgaray maintained that Trump's move was "good news for Mexico," which is eager to renegotiate the deal.

"We are prepared, we are ready to work together with both the governments of the U.S. and Canada to make our trade agreement better," Videgaray said. "Better for the people of Mexico, the people of the U.S., and the people of Canada. We understand that this is a 25-year-old agreement that was negotiated. The world has changed. We've learned a lot and we can make it better. We can make this a negotiation that is good for the three partners involved, certainly, under a win-win framework."

Videgaray also restated the need for Mexico to forge a stronger economic relationship with China in light of Trump's policy statements. "We will continue on that path, we will continue to get closer to China, we will continue to seek investment and we will continue to expand opportunities so that Mexican exporters can increase their access to that big Asian market," he said in February. "Within [the area of] foreign policy, now more than ever there is an urgent need to diversify our ties with the outside beyond North America, especially our economic, trade and investment ties."

China's economic engagement in Mexico is part of a pattern of investment in Latin America that some experts worry could give them control over critical technologies and complicate efforts to fight political corruption in the region.