Mexican President Andrés Manuel López Obrador said Tuesday he believes a deal is close that would end the Trump administration's threat to impose tariffs on Mexico in response to illegal immigration.

“There are signs that it matters to the U.S. officials that there’s a deal,” he told reporters. “I think the meeting tomorrow will be important and that there will be a deal before June 10, before this tariff comes into effect."

President Trump said Thursday he would place a 5% tariff on all Mexican goods, increasing 5% every month until the “illegal immigration problem is remedied.” Business groups and GOP lawmakers have called on the president to back away from the threats, saying the tariffs would likely harm the U.S. economy without resolving the border issue. Mexico has warned of possible trade retaliation of its own.

Mexican officials, lead by Foreign Minister Marcelo Ebrard, are in Washington, D.C., in hopes of negotiating a compromise. Ebrard did not give any details about what the proposed compromise may look like, but said he was optimistic. "We’re going to find common ground, I think," he told reporters.

Ebrard rejected a proposal floated by U.S. officials that would involve Mexico being designated a "safe third country" for the immigrants, meaning that refugees passing through Mexico to the U.S. would first have to claim asylum in Mexico. The U.S. has a similar agreement with Canada. Many of the immigrants to the U.S. in the current border crisis originate from Central America.

Trump's threatened tariffs came the same day that the Mexican Senate began the process to ratify the U.S.-Mexico-Canada Agreement, a top trade policy goal of the White House that would replace the 1993 North American Free Trade Agreement. While Thursday's announcement has not derailed consideration of the USMCA deal, Jesús Seade, Mexico’s deputy foreign minister for North America, warned Monday that new tariffs could be a “stumbling block” regarding its passage.

[Opinion: Trump's Mexico tariffs could 'cripple' US auto industry, raise average price of cars by $1,300]