WASHINGTON/MEXICO CITY (Reuters) - U.S. President Donald Trump threatened to make Mexican immigration control a condition of a new NAFTA trade deal on Monday, even as ministers from Canada, the United States and Mexico readied a fresh push to finalize a revamped accord this week.

FILE PHOTO: U.S. President Donald Trump waves as he arrives on Air Force One at Joint Base Andrews in Maryland, U.S., upon his return to Washington from Palm Beach, Florida, April 22, 2018. REUTERS/Yuri Gripas

“Mexico, whose laws on immigration are very tough, must stop people from going through Mexico and into the U.S. We may make this a condition of the new NAFTA Agreement,” Trump wrote in a Twitter post. “Our Country cannot accept what is happening!”

Trump made similar comments linking the North American Free Trade Agreement (NAFTA) and immigration when a ‘caravan’ of migrants from Central America moved through Mexico earlier this month. “They must stop the big drug and people flows, or I will stop their cash cow, NAFTA,” Trump wrote in an April 1 Twitter post.

However, discussion of immigration controls has not been a part of formal negotiations on the new NAFTA accord, and talks by all accounts - including Trump’s - are progressing.

Mexican Foreign Minister Luis Videgaray dismissed Trump’s comment in his own Twitter post. Mexico decides its immigration policy in a sovereign manner, he said, and it would be “unacceptable” to condition the renegotiation of NAFTA.

Before Trump’s tweet, Mexican President Enrique Pena Nieto said he hoped for agreement soon on a reworked NAFTA.

Speaking in Germany, Nieto said differences between the parties could be overcome to revamp the 24-year-old accord, which underpins some $1.2 trillion in annual trilateral trade.

Canada’s Foreign Minister Chrystia Freeland told a news conference in Toronto that she would be traveling to Washington on Tuesday to meet with Mexican Economy Minister Ildefonso Guajardo and U.S. Trade Representative Robert Lighthizer.

“We have for the past few weeks been involved in intensive negotiations. This is a phase of very, very energetic work by Canada and we will be continuing that at the ministerial level in Washington,” said Freeland.

Guajardo and others have said a NAFTA deal could be possible by early May, and officials hailed progress made on the key issue of new automotive sector rules last week.

Even so, differences still remain on U.S. demands to change dispute resolution mechanisms, and other issues.

“The U.S. still needs to be more flexible so there are conditions to create jobs in Mexico, the United States and Canada,” said Juan Pablo Castanon, head of the Consejo Coordinador Empresarial, the umbrella group representing Mexican private sector interests at the NAFTA talks.

It was too early to say when a deal could come, he added.

A Mexican source close to the talks, speaking on condition of anonymity, said a deal was unlikely for Tuesday, adding that “two to three days of work” between negotiators and ministers were still needed.

DWINDLING CARAVAN

Since peaking at about 1,500 people, the so-called caravan of migrants has dwindled under pressure from Trump and Mexican authorities, who vowed to separate those migrants with a right to stay in Mexico from those who did not.

One group of several hundred migrants could reach the U.S. border by Tuesday or Wednesday.

“If members of the ‘caravan’ enter the country illegally, they will be referred for prosecution for illegal entry in accordance with existing law,” Homeland Security Secretary Kirstjen M. Nielsen said in a statement on Monday.

U.S. Attorney General Jeff Sessions said in a statement he had directed officials to beef up the numbers of prosecutors and immigration judges at the border to deal with any increased workload from the caravan.