Mexico said it averted the so-called 'safe third country' designation with the United States after U.S. Secretary of State Mike Pompeo praised Mexican efforts in reducing U.S.-bound migrant flows. 

However, Pompeo, while praising Mexico's efforts, said there was still "more work to do." 

Pompeo met with Mexican Foreign Minister Marcelo Ebrard on Sunday in Mexico City amid heightened bilateral tensions ahead of a July 22 deal deadline that removed tariff threats on Mexican exports. 

An agreement reached in June laid out that if the U.S. deems that Mexico has not done enough to thwart migrants by the deadline, the two countries would begin talks over changing rules to make most asylum seekers apply for refuge in Mexico, not the United States. 

Ebrard said considering the advances Mexico had made, it was not necessary to "initiate any type of negotiation on a 'safe third country' agreement between Mexico and the United States." 

Pompeo, however, was less definitive. He praised the progress made by Mexico in helping cut apprehensions on the U.S. southern border by an almost a third last month but added: "We've got a long way to go yet. There's still much more work to do." 

"As for the next set of actions, I'll talk with the president and the teams back in Washington and we'll decide exactly which tools and exactly how to proceed," Pompeo said at a news conference in San Salvador, the last leg of a short Latin American tour. 

Mexico argues it has followed through on its commitment to reduce migration from Central America, underscoring that apprehensions of migrants on the southern U.S. border dropped roughly a third to about 100,000 in June. 

Mexico has deployed some 21,000 militarized National Guard police to decrease the flow of undocumented people. 

Under the agreement, Mexico averted punitive tariffs on U.S.-bound Mexican shipments threatened by U.S. President Donald Trump with the promise to cut the number of illegal migrants traveling from Central America to the U.S. border. 

The meeting between the nations' two top diplomats came a day before the end of the 45-day period and as U.S lawmakers wrangle over a regional trade deal meant to replace the current North American Free Trade Agreement (NAFTA). 

"We have said once and again that we are not ready to sign" any such safe third country agreement, Martha Barcena, the Mexican ambassador to Washington said on Thursday.

Trump has made immigration a cornerstone of his presidency and pledged to build a wall on the southern border with Mexico in his 2016 run for office. He has since fought with Congress and in the courts for funding to pay for it. 

His administration announced sweeping new asylum rules last Monday that bar almost all immigrants from applying for asylum at the U.S.-Mexico border by requiring them first to pursue safe haven in a third country through which they had traveled on the way to the United States. 

However, Mexico has long resisted U.S. pressure to formally accept the safe third country status.