 -- Donald Trump said that while he had a "substantive, direct and constructive" meeting with Mexican President Enrique Pena Nieto, they "didn't discuss" who would pay for the border wall that Trump has made a centerpiece of his presidential campaign.

Trump arrived in Mexico City this afternoon and took the microphone for a press conference alongside Pena Nieto.

"I was straightforward in presenting my views about the impacts of current trade and immigration policies on the United States" Trump said. "We are united by our support of Mexicans."

"I have a tremendous feeling for Mexican-Americans not only in terms of friendship but also in terms of the numbers I employ," he said. "I am proud to say how many people I employ."

Trump said they "didn't discuss" who would pay for the wall that he has repeatedly said he plans to build along the U.S.-Mexico border.

He said, "Having a secure border is a sovereign right and mutually beneficial. We recognize and respect the right of either country to build a physical barrier or wall on any of its borders to stop the illegal movement of people, drugs and weapons."

Pena Nieto spoke first, praising the democratic process and saying that Mexico will be a good neighbor to the United States and that the countries will work together as "strategic allies."

"We must always be open to talk about what has worked and what hasn't," he said in Spanish. He said the countries will have a "relationship based on mutual respect" and recounted that during their private meeting he said he would stand by Mexicans "wherever they are."

Referring to Trump, Pena Nieto said that "we may not be in agreement on a number of subjects" but the two countries are important to each other. He said the purpose of their meeting was to meet and talk about their views. He called their meeting "very open and constructive."

He said that he wants to make the border "more efficient and more secure" with the next president and that strengthening the border was important to Mexico.

Trump announced his intentions to visit Mexico on Tuesday night, posting on Twitter, "I have accepted the invitation of President Enrique Pena Nieto, of Mexico, and look very much forward to meeting him tomorrow."

Trump's campaign manager, Kellyanne Conway, denied that the trip was as last minute as it seemed, saying the invitation from Pena Nieto came late last week. Democratic presidential nominee Hillary Clinton has been invited to meet with Pena Nieto as well.

"Well, maybe it's been revealed publicly last minute, but the fact is that Mr. Trump was very excited to accept the invitation from the president in Mexico. It's a decisive presidential move. He wants to establish a conversation with a neighboring country, a leader. And also to discuss the common problems and challenges that our country is facing," Conway said during an interview with NBC.

She said today's Trump would be "very presidential."

"I think they’ll have a productive conversation today ... illegal immigration but also trade policy and drugs," Conway said.

The real estate mogul was joined by former New York City Mayor Rudy Giuliani and Sen. Jeff Sessions, the Trump campaign said Tuesday.

On Aug. 16, Pena Nieto said of Trump, "I have never met him. I can't agree with some of the things he has said, but I will be absolutely respectful and will seek to work with whoever becomes the next president of the United States."

During a town hall with Fox News' Sean Hannity last week, Trump was asked about Pena Nieto's comment.

"I'd meet with him," Trump said. "Absolutely, I'd meet with him."

Pena Nieto said in March that he would not pay for a border wall under any circumstances.

Trump is scheduled to speak on immigration later this evening in Phoenix, joined by his running mate, Gov. Mike Pence. Trump's policies on immigration, what has become his trademark issue, have become murky in recent weeks, with Trump indicating that he may not deport all undocumented immigrants, as he once suggested.

This is a developing story. Please check back for updates.

ABC News' John Santucci and David Caplan contributed to this report.