US President Donald Trump renewed his threat on Monday to impose tariffs on Mexico as controversy erupted over what exactly is in the countries’ new migration deal, which the Mexican government admitted would be reviewed in 45 days.

Trump reignited the pressure three days after granting a reprieve from tariffs that he had threatened to apply from this week to force the major US trading partner to boost measures against illegal immigrants trying to enter the US.

In a series of statements and tweets, Trump alluded to still-secret provisions in the deal that he said would need approval by the Mexican Congress.

“If for any reason the approval is not forthcoming, Tariffs will be reinstated!” he tweeted.

Faced with a surge of Central American immigrants fleeing poverty and gang violence, Trump had already declared a national emergency in an effort to build his promised border wall with Mexico, and had also more than once threatened to shut the frontier before mooting the tariffs.

The president did not go into details Monday, but Mexico said it had agreed to discuss one of Trump’s top demands, a so-called “safe third-country agreement” – in which migrants entering Mexican territory must apply for asylum there rather than the US – if the flow of undocumented Central Americans continues.

Foreign Minister Marcelo Ebrard, who led the Mexican negotiating team in Washington last week, said he had rebuffed the US demand for such a measure, but agreed to revisit the matter in 45 days.

“In the meeting with the vice president of the United States, they were insistent on the safe third-country issue,” Ebrard told a press conference.

“We told them – I think it was the most important achievement of the negotiations – ‘let’s set a time period to see if what Mexico is proposing will work, and if not, we’ll sit down and see what additional measures [are needed]’,” he said.

Told by reporters at the White House that Mexico has not confirmed its legislature will vote on the unspecified further measures, Trump answered: “I don’t think they’ll be denying it very long.”

Under the deal, Mexico agreed to bolster security on its southern border and expand its policy of taking back asylum-seekers as the US processes their claims.

Trump angrily rebuffed criticism over a New York Times report that said the main terms of the deal were not new, and had in fact been agreed on months before his tariff threat.

Secretary of State Mike Pompeo sidestepped controversy, instead praising Mexico and highlighting what he said was an example of “diplomacy at its finest”.

“It’s the biggest effort to date that the Mexicans have committed. It’s something that we pressed for,” he said. “We will work closely with them to make sure that that is a successful effort.”