Vice President Mike Pence was quoted Thursday by the Associated Press as saying he was encouraged by the latest Mexican proposals but added that the 5% tariffs are still scheduled to be imposed Monday and go up "if we don't see the results we need to see".
The statistics, usually announced in the second week of each month, were released before the Wednesday meeting, as the USA government is pressuring Mexico to curb the flow of immigrants, many of whom originated from central American countries.
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Ebrard said he's optimistic about the talks continuing Thursday.
The two sides are in discussions led by US Vice-President Mike Pence in an effort to strike a deal that would satisfy Mr Trump.
"The U.S. authorities have behaved very well, President Trump, because they haven't closed themselves off to dialogue and we hope that a deal is reached today", he said.
States like New Mexico has been facing escalating violence from drug cartels.
The United States slapped up to 25% tariffs on $200 billion (£157 billion) in Chinese imports last month, prompting Beijing to levy its own tariffs on $60 billion in American goods.
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As of Thursday, US Customs and Border Protection had still not received guidance necessary to implement the tariffs, including details like software changes for automated systems that process the customs entries, according to trade and customs attorney Lenny Feldman, who is on CBP's commercial customs operations advisory committee.
Mexican Foreign Minister Marcelo Ebrard said the Mexican government had offered to send 6,000 members of the National Guard to secure its southern border with Guatemala.
Economists, many Republican lawmakers and business leaders have warned that the escalating tariffs would raise prices for us consumers and damage both nations' economies.
Mexican Foreign Secretary Marcelo Ebrard said immigration, not tariffs, was the main focus at the White House meeting, which included Secretary of State Mike Pompeo, Vice President Mike Pence and other USA officials.
The Mexican and USA officials described the accord's framework on the condition of anonymity, citing the sensitivity of the worldwide negotiations, but they expressed optimism that the deal was attainable.
Officials said the final decision rests with Trump, who is scheduled to return on Friday from his European trip to commemorate D-Day and has been regularly briefed on negotiations while overseas.
USA stocks and Treasury yields spiked higher on Thursday after Bloomberg News reported that the United States is considering a delay in the tariffs as talks continue, citing people familiar with the matter.
In a sign of a wider crackdown, the leftist administration of Mexican President Andres Manuel Lopez Obrador said earlier that it blocked the bank accounts of 26 people for alleged links to human trafficking, while it detained on Wednesday at least 350 migrants crossing into Mexico and arrested two prominent migrant rights activists. State and local police provided a security escort to the migrants as they walked along a highway leading from the border to the first major city in Mexico, Tapachula.