It also acknowledged the two presidents' "clear and very public differences" on who will pay for the border wall.
"Both presidents have instructed their teams to continue the dialogue to strengthen this important strategic and economic relationship in a constructive way," the statement read.
Trump spoke to Peña Nieto by phone for nearly an hour.
"I will say that we had a very good call," Trump said in a news conference at the White House. "I've been very strong on Mexico. I have great respect for Mexico. I love the Mexican people."
Trump added, "As you know, Mexico with the United States has out-negotiated us and beat us to a pulp through our past leaders. They've made us look foolish."
Later that day, Peña Nieto announced on Twitter that he had informed Trump that he would not attend their scheduled business meeting.
During his speech at the Republican retreat in Philadelphia Thursday, Trump said he and Peña Nieto "agreed" to cancel their planned meeting.
Trump, however, said today that he and Peña Nieto have a "good relationship."
"We have really, I think, a very good relationship, the president and I," Trump said in his news conference, adding, "We are going to be working on a fair relationship and a new relationship."
During Trump's press conference with British Prime Minister Theresa May, the Mexican government released a statement in Spanish. It said the U.S. and Mexico had agreed “for now to not speak publicly" about who will fund Trump's proposed wall on the Mexican border.
Later in the day, White House press secretary Sean Spicer told reporters Trump agreed with the Mexican president that they will not speak publicly about how the U.S.-Mexico border will be paid for.
“They agreed not to discuss how it would be paid for publicly, that they would continue to have those discussions privately," Spicer said.
ABC News' Jordyn Phelps contributed to this report.