May and Trump are said to have discussed trade, security, and the future of the two countries' relationship.
The move is not especially welcome in Mexico, in part because Trump has vowed to make Mexico pay the cost of building the barrier.
Trump had tweeted on Thursday that it would be better for the Mexican leader not to come to Washington if Mexico would not pay for the wall. "In fact, we now tax exports, not imports", Spicer told the Washington Post on Thursday.
Throughout his campaign, Trump insisted that Mexico would pay for the wall but did not offer evidence of how the country would be coerced in to doing so.
"The statement went on to express Mexico's respect and admiration for the Jewish people, and especially for the great Mexican Jewish community, which contributes every day to the construction of a freer, fairer and more prosperous Mexico".
A man stops to read headlines, many featuring U.S. President Donald Trump's actions to jump-start construction on a promised border wall and his insistence that Mexico will foot the bill, in Mexico City, Jan. 26, 2017.
But that is exactly what one of US President Donald Trump's ideas on how to fund a US-Mexico border wall has given rise to. He reiterated Wednesday that Mexico - which has repeatedly said it will not pay for the wall - will pay for it "100 percent".
Since he first proposed the idea to build an "impenetrable, physical, tall, powerful, beautiful, southern border wall" between the United States and Mexico, Mr Trump has insisted Mexico will pay. Mexico has repeatedly said it will not pay for the wall.
Without mentioning the trip, Pena Nieto said he would wait for a report from a high-level Mexican delegation holding meetings in the United States capital this week and consult with governors and MPs before deciding on "the next steps to take". But he said regarding trade, "Mexico has outnegotiated us and beat us to a pulp".
Those coming into the USA from the south are seeking better economic condition and include people fleeing El Salvador and other parts of Central America, ravaged by poverty, violence and other consequences of the region's drug wars. Mexican workers are excellent, he said, and earn less than those in China.
Mr. Trump also tweeted that the US has a $60 billion trade deficit with Mexico. They have made us look foolish.
"If we turn our backs on trade, it's going to hurt our economy, and it's going to particularly hurt Colorado", Gardner said.