"There is a good chance" that the U.S. will be able to make a deal with Mexico, averting tariffs that could go into effect next week, President Trump tweeted Friday, as he traveled back to the U.S. from Europe.

"If we are able to make the deal with Mexico, & there is a good chance that we will, they will begin purchasing Farm & Agricultural products at very high levels, starting immediately," Mr. Trump tweeted. "If we are unable to make the deal, Mexico will begin paying Tariffs at the 5% level on Monday!"

However, this tweet contradicts assertions the White House has repeatedly made that the tariffs are a response to an immigration issue, not a trade issue. The president has said he would impose tariffs on Mexico because it has not done enough to stop the flow of illegal immigration through the southern border. This is why Customs and Border Patrol is to give official notice of the tariffs.

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Prior to the president's tweet, there had been no indication that trade -- increased agricultural exports to Mexico -- was part of the tariff discussion.

The president has defended his threat to impose steep new tariffs on all goods imported from Mexico, rejecting concerns of economists and some fellow Republicans that the proposed increase of up to 25% could hurt U.S. businesses and consumers as much as it punishes Mexico. Mr. Trump is threatening to slap tariffs on all Mexican imports beginning Monday, starting at 5%, unless Mexico stems the flow of migrants reaching the U.S. southern border.

"Tariffs are a beautiful thing. It's a beautiful word if you know how to use them properly," Mr. Trump told Fox News host Laura Ingram on Thursday in France, where he was taking part in 75th D-Day anniversary commemorations.

Mr. Trump said the U.S. Congress bears some of the blame for the circumstances at the border, where record numbers of migrants -- primarily from El Salvador, Honduras and Guatemala -- have crossed illegally into the U.S. in recent weeks from Mexico. But he said Mexico was also culpable, "because they are letting people walk up through their country and they shouldn't let anybody walk up through their country."

"Now I've told Mexico if you don't stop this onslaught, this invasion -- people get angry when I use the word 'invasion,' people like Nancy Pelosi that, honestly, they don't know what the hell they're talking about," Mr. Trump said, taking a new shot at his rival, the Democratic Speaker of the House of Representatives.

The president accused Mexico, through what he views as inadequate enforcement of its own borders, of allowing "an invasion without guns" across the U.S. frontier.

"They send in $500 billion worth of drugs, they kill 100,000 people. They ruin a million families every year," Mr. Trump claimed. "If you look at that, that's really an invasion without the guns."

On Thursday U.S. officials told CBS News that Mexico's government had offered to deploy 6,000 troops along its own southern border and to overhaul its asylum laws in a bid to appease the Trump administration and avoid the new tariffs being imposed on Monday. There has reportedly been debate within the Trump administration about delaying the June 10 deadline, but White House press secretary Sarah Sanders said Thursday that the U.S. was "still moving forward with tariffs at this time."

Mr. Trump dismissed concerns that hiking tariffs on Mexican imports could hit U.S. consumers and manufacturers, claiming instead that if they were imposed the U.S. would, "make a fortune, because all the companies are going to move back into the country."

The impact of tariffs

CBS News' MoneyWatch reported on Thursday, however, that many U.S. companies, especially small to medium size manufacturers, would struggle to absorb the costs of moving their operations out of Mexico, and struggle even more to move those operations onto U.S. soil where labor costs are much higher.

Michelle Casario, an assistant professor of economics at Villanova University, told CBS News this week that if even the first-tier 5% tariff is levied on imports from Mexico, American "consumers could expect to see higher prices from avocados to tomatoes, beer to tequila, phones to computers to televisions, and even higher prices at the gas pump," due to how intertwined the neighboring nations' economies have become during 25 years of free trade.

Due to those concerns, and the fact that any reciprocal tariffs imposed by Mexico could hurt American farmers who export south of the border, Mr. Trump faces considerable opposition within his party. In the Senate, at least, it's possible that Republicans could try to block him from moving forward with the planned tariff hike.

Mr. Trump told Fox News that such opposition from Congress -- including from his own party members -- was diminishing his bargaining power as his administration negotiates with the Mexican government to get it to crack down on the migrant flow.

The president said Congress, "should be saying, 'we are with the President, we will do whatever he wants to do,' and Mexico would fold like an umbrella."

Instead, Mr. Trump complained that, "I have these people -- and I'm saying there are some Republicans, too -- I think they should be ashamed of themselves… they come out and they talk about 'tariffs are bad,' so, they are killing-- they are hurting my negotiation."

Weijia Jiang and Kathryn Watson contributed to this report.