President Trump and Mexican President Enrique Peña Nieto in Mexico City in in August 2016In his first meeting as president with his Mexican counterpart, Donald Trump on Friday said he "absolutely" intends&nbsp;for Mexico to pay for the controversial wall he wants to build along the United States' southern border.Trump and Mexican President Enrique&nbsp;Pe&ntilde;a&nbsp;Nieto&nbsp;met on the sidelines of the Group of 20 summit here, amid sharp disagreements over trade and immigration. Some officials&nbsp;had hoped the brief encounter could help heal badly soured relations between the two neighbors.The proposed wall continues to make that&nbsp;difficult.As journalists were allowed in to see the two leaders take their seats&nbsp;ahead of&nbsp;their meeting, one reporter asked Trump if he still wanted Mexico to pay for the wall."Absolutely," Trump said.Mexico has repeatedly said it will not pay for a new border barrier. Despite Trump's statement, his administration has asked Congress for money to pay for building portions of a wall along the border. So far, that request has met with a chilly reception on Capitol Hill.Homeland Security Department officials have made clear that the administration does not intend to build a wall along the full length of the border, the way Trump often has described it.In January,&nbsp;Pe&ntilde;a&nbsp;Nieto canceled a scheduled first meeting&nbsp;when Trump threatened to impose a tax on Mexican imports to pay for the&nbsp;wall, one of his key campaign promises.Before Trump responded to the reporter's question on Friday, the two presidents delivered prepared statements.&nbsp;Trump referred to Pe&ntilde;a Nieto&nbsp;as a "friend." He said he was "negotiating" changes&nbsp;in the landmark 1994 North American Free Trade&nbsp;Agreement "and some other things with Mexico and we&rsquo;ll see how it all turns out but I think we've made very good progress."Mexico has said it is willing to renegotiate elements of NAFTA. Canada is also a signatory.Speaking through a translator, Pe&ntilde;a&nbsp;Nieto said the meeting will help the two countries continue a "flowing dialog" especially "for the security of both nations, especially for our borders."He noted that "migration" is an issue of concern to both administrations.&nbsp;And he added that "it is the co-responsibility to deal with organized-crime issues."The day he declared his candidacy, Trump characterized many Mexicans as rapists and criminals who should be kept out of the U.S. Opposition to Mexican immigration to the U.S. became a hallmark of his campaign.&nbsp;Though enduring a brutal wave of violence, some of it related to drug trafficking, Mexico is nevertheless one of the United States' largest trading partners, shares long and strong cultural ties and enjoyed relatively good diplomatic relations and security cooperation with Washington before Trump took office.The two men met last year when Trump was a candidate. He traveled to Mexico City in August in a visit that many Mexicans saw as disastrous. Trump&nbsp;contradicted&nbsp;Pe&ntilde;a&nbsp;Nieto&nbsp;on the wall&nbsp;and seized control of a news conference, calling on American reporters and ignoring the Mexicans as the Mexican president looked on helplessly.Pe&ntilde;a&nbsp;Nieto's domestic favorability ratings dropped to an all-time low afterward.The two have also shared several telephone calls, some quite contentious. In one, according to an official who listened in, Trump suggested that he'd&nbsp;send U.S. troops to Mexico to fight drug traffickers if Mexico's army didn't step up. Nothing could be more anathema to Mexicans' sense of sovereignty and nationalism.Even before Friday's encounter, expectations in Mexico were low that it would be a chance to reset the two governments' troubled relations.&nbsp;One prominent newspaper, El Financiero, said talking to Trump is a "conversation with a deaf man.""Undoubtedly, a meeting of presidents is always important ... but this will not be an encounter in which there will be major agreements," Mexican Foreign Minister Luis Videgaray&nbsp;said ahead of Friday's session. "We should not expect anything substantative."Despite the formal and public tension, other officials in the U.S. and Mexican governments are working more closely. Videgaray sustains a close&nbsp;relationship with presidential son-in-law and advisor Jared Kushner. Secretary&nbsp;of State&nbsp;Rex Tillerson&nbsp;and Homeland Security Secretary John Kelly have traveled to Mexico City several times and received their counterparts in Washington.The American officials often find themselves in the position of smoothing over the more provocative statements about Mexico and its citizens made by&nbsp;their boss, the president.&nbsp;Bennett reported from Hamburg, Wilkinson from Washington.