Donald Trump said he didn't push Mexican President Enrique Pena Nieto on who would pay for the border wall he wants to build as president, and instead said he hopes the two countries can work closely together to secure the southern border and bring jobs back to both countries.

"We did discuss the wall," Trump told reporters at a joint press conference with Nieto. "We didn't discuss payment of the wall. That'll be for a later date. This was a very preliminary meeting. I think it was an excellent meeting."

Trump has made Mexico paying for a wall along the border a central campaign promise. But the visit did showcase the Republican presidential nominee appearing diplomatic and showing he could work with those who disagree with him.

"The bond between our two countries is deep and sincere and both our nations benefit from a deep and honest relationship between our two governments," Trump said.

Trump said the U.S. and Mexico have five shared goals: ending illegal immigration, securing the border, dismantling the drug cartels, improving NAFTA, and keeping wealth in the western hemisphere as much as possible.

Trump and Nieto were joined by former New York City Mayor Rudy Giuliani and Alabama Sen. Jeff Sessions for a meeting that lasted more than an hour and was later described as "very open and constructive" by the Mexican president.

"We have made tremendous progress in recent years working closely with President Obama and with the next administration we should step up our efforts to make sure the U.S.-Mexico border is [inaudible] and secure," Nieto said in his own remarks after speaking with Trump.

"I am confident that moving together and forward, we can be more prosperous and secure than ever before — never losing sight of the fact that freedom and independence are the indispensable bond we cherish," he added.

While the two men made no effort to conceal their disagreements over trade and Trump's proposal to build a border wall, they both spoke of improving the relationship between America and its Southern neighbor and the two countries' shared border.

"We share the busiest border in the world, crossed legally every day by more than 1,000 vehicles," Nieto said. "Both countries should be investing more on the border — more infrastructure, more people and more technology."

Trump expressed his admiration for the Mexican people and millions of Americans of Mexican ancestry, noting how many he has employed at his businesses.

When it was his turn to talk trade, Trump reiterated that he believes agreements like NAFTA should be "updated to reflect the realities of today."

"There are many improvements that can be made that would make both Mexico and the U.S. stronger and keep industry in our hemisphere," he said, shortly after Nieto expressed his full belief "that NAFTA has been good" for both countries.

"I do not belive trade should be treated as a zero-sum," Nieto told reporters.

Trump's first official meeting with the Mexican president came hours before he was expected to touch down in Phoenix, Arizona for a major speech on his own immigration policy. Nieto said Wednesday that he enjoyed getting to know the Republican presidential hopeful better and looked "forward to meeting again with Mrs. [Hillary] Clinton," whom he worked with during her tenure as secretary of state.

"We may not agree on several issues, but your presence here, Mr. Trump, shows we have a fundamental coincidence — our countries need each other," Nieto said directly to the candidate. "The United States is very important for Mexico just as Mexico is very important for the United States."