Mexican officials were seeking to persuade the White House in talks hosted by US Vice President Mike Pence on Wednesday that their government has done enough to stem immigration and avoid looming tariffs.

US authorities at the southern border with Mexico have become overwhelmed in recent years by an increase in mostly Central American families and unaccompanied minors seeking asylum to escape violence back home.

Frustrated by the lack of progress on a signature issue from his 2016 presidential campaign, Donald Trump unexpectedly announced last week that he would impose 5 percent tariffs on all imports from Mexico, rising to as much as 25 percent later in the year, unless Mexico took a harder line.

Trump, who was in Britain to commemorate the anniversary of the D-Day landings on Wednesday, said in London on Tuesday that it was "likely" that the first wave of tariffs, set for next week, would go ahead. 

He has faced significant pushback from his own Republican party, however, with many lawmakers concerned about the effect that such tariffs would have on cross-border trade and US businesses and consumers.

They warned the White House not to count on the same level of backing it got earlier this year, when Trump declared a national emergency to divert funds to build barriers at the border.

"We're not real fond of tariffs, so don't assume you can have the exact same level of support. That was my basic message," Senator Ron Johnson told reporters after a meeting between lawmakers and White House officials on Tuesday.

The tariff threat has also raised questions over the future of a three-way deal with Canada to replace the North American Free Trade Agreement, concluded after a year of negotiations. Pence is the Trump administration's point person for getting Congress to approve the new deal, known as USMCA, which he has pledged will happen in 2019.

Mexican Foreign Secretary Marcelo Ebrard was expected to attend the talks, which was expected to take place in Washington on Wednesday afternoon. He has said the threatened tariffs would be devastating to Mexico's economy and would not stop the waves of migrants from crossing the southern US border.

The Mexican delegation was expected to try to show the White House that authorities are taking steps to stem the flow of migrants, with Mexico detaining double the number per day than it was a year ago.