US President Donald Trump said on Sunday that his administration will release additional details of its agreement with Mexico on immigration issues that allowed the country to avoid US tariffs.

"Some things not mentioned in yesterday's press release, one in particular, were agreed on. That will be announced at the appropriate time," Trump said in a series of tweets, without elaborating on details.

"There is now going to be great cooperation between Mexico & the USA, something that didn't exist for decades," the president wrote, adding that his administration "can always go back" to the previous position of imposing tariffs against Mexican imports if that doesn't happen.

Following several days of negotiations in Washington, the United States and Mexico reached an agreement on Friday to avert the threat of tariffs on all Mexican imports on Monday.

As part of the deal, Mexico will deploy its National Guard throughout the country to curb irregular migration, giving priority to its southern border. The United States will immediately expand a program to allow asylum-seekers to remain in Mexico while their legal cases proceed.

The New York Times reported on Saturday that the deal consisted largely of actions that Mexico over the past several months had already promised to take, citing officials from both countries familiar with the negotiations.

But Trump called it "another false report." "We have been trying to get some of these Border Actions for a long time, as have other administrations, but were not able to get them, or get them in full, until our signed agreement with Mexico," he said in Sunday's tweets.

"I have full confidence, especially after speaking to their President yesterday, that they will be very cooperative and want to get the job properly done," Trump said.

Trump on Saturday also claimed that Mexico had agreed to immediately begin buying large quantities of US agriculture products, although that was not included in the US-Mexico Joint Declaration released on Friday.

Three Mexican officials said Saturday they were not aware of any side accord in the works, and that agricultural trade hadn't been discussed during three days of negotiations in Washington, according to Bloomberg.