President Trump is returning from a trip to Europe and will be briefed on the talks when he returns, according to White House officials.
The announcement avoids what economists and Republicans feared would be damaging to the US economy.
"This new proposal is not good for Toyota", said Barr.
U.S. President Donald Trump says he has suspended plans to impose tariffs on Mexico, tweeting that the country "has agreed to take strong measures" to stem the flow of Central American migrants into the United States. However, one of the U.S.'s main demands, that Mexico agree to becoming a "safe third country" for asylum seekers, remained a key topic during Friday's talks, those monitoring the situation said.
At least half a dozen Republican senators spoke out against the tariffs at the GOP meeting, and many more have been sharply critical of the president's trade policies.
Talks had gotten off to a shaky start Wednesday, as the USA once again pressed Mexico to step up enforcement on its southern border with Guatemala and to enter into a "safe third country agreement" overhauling its asylum system.
Typically, the White House would allow time for agencies and importers to sort out the changes, but with the tariffs not yet finalized, businesses will have only the weekend to work out any changes.
While Trump said progress was made during Wednesday's 90-minute meeting and that "something pretty dramatic could happen" in the coming days, he continued to hold out the threat that the US will follow through with tariffs.
"There is not much support in my conference for tariffs - that's for sure", said Senate Majority leader Mitch McConnell, R-Ky., adding that he hoped negotiations with Mexico would be "fruitful" and that tariffs would be avoided.
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Mark Meadows calling the move "another openly desperate move to resuscitate a dead collusion conspiracy". He did not indicate whether the House would try to compel Mueller's testimony with a subpoena.
Short said, however, that "there's a long way to go still" before an agreement can be reached. "They need to keep the pressure where it needs to be applied".
At the same time, it's not at all clear the tariffs would check the rising number of migrants at the border, a crisis that has vexed the White House.
He said he'd talked to Kentucky farmers who are anxious and that there's "gathering momentum" among farm state Republicans.
In an interview that aired late Thursday with Fox News from France where he is attending D-Day commemorations, Trump defended his tariff plan as "a handsome thing" and complained about "this onslaught, this invasion" of undocumented migrants.
The United States slapped tariffs of up to 25% on $200 billion in Chinese imports last month, prompting Beijing to levy its own tariffs on $60 billion in American goods. Trump has said the tariffs will be enacted on Monday. There are four major auto assembly plants in the state, employing almost 95,000 people.
AMLO, as he's known, said on Friday that national guard troops will be stationed at Mexico's southern and northern borders.
He said he's also anxious that tariffs would hurt efforts to get the trade package approved.
But in the United States capital, negotiators holding a second day of talks were still trying to find agreement on issues including asylum application procedures and financial aid to the Central American countries that are the source of most of the migrants. "The Tariffs scheduled to be implemented by the US on Monday, against Mexico, are hereby indefinitely suspended".
It's a crossroads for the GOP as the White House is taking the party in a confrontational new direction.