WASHINGTON - A White House trade adviser and a leading Republican senator said on Wednesday that a U.S. plan to impose tariffs on Mexican goods might not go into effect, offering hope for Mexico and American businesses concerned about economic damage from a new front in President Donald Trump's trade wars. Adviser Peter Navarro told CNN that Trump's threatened tariffs, due to come into force next week, might not be needed because the United States now has "the Mexicans' attention" on stemming illegal immigration. Frustrated by the lack of progress on a signature issue from his 2016 election campaign, Trump unexpectedly told Mexico last week to take a harder line on curbing illegal immigration or face 5% tariffs on all its exports to the United States, rising to as much as 25% later in the year. Mexican officials will seek to persuade the White House in talks hosted by U.S. Vice President Mike Pence on Wednesday that their government has done enough to stem immigration and avoid looming tariffs. Speaking in Ireland, Trump said he thinks Mexico wants to make a deal to avert the tariffs but that if it does not take steps to control the flow of migrants the duties will go into effect. "Mexico can stop it. They have to stop it, otherwise we just won't be able to do business. It's a very simple thing. And I think they will stop it. I think they want to do something. I think they want to make a deal, and they sent their top people to try and do it," Trump said. Mexican President Andres Manuel Lopez Obrador said he was optimistic the talks can end in an agreement. "We believe that these tariffs may not have to go into effect precisely because we have the Mexicans' attention," Navarro said. Trump has faced significant resistance within his own Republican Party over the threatened tariffs, with many lawmakers concerned about the potential impact on cross-border trade and on U.S. businesses and consumers. Chuck Grassley, the Republican chairman of the U.S. Senate Finance Committee, predicted that the United States and Mexico would strike a deal to avert the tariffs. Mexican officials will offer a "long list of things" to avoid the duties in talks this week with their American counterparts, Grassley told reporters, adding that he thinks a possible deal could be announced on Thursday night. Grassley represents the farming state of Iowa, which exports pork and other agriculture products to Mexico and might be hit by Mexican retaliation in a prolonged trade dispute. Trump, who in Britain on a state visit this week, said in London on Tuesday it was likely that the first wave of tariffs, set for June 10, would go ahead. Pence is looking for a comprehensive suite of proposals from the visiting officials about stopping the flow of migrants from Central America, a White House official said. "Trade and all other aspects of our relationship are critically important, but national security comes first and the White House is dead serious about moving forward with tariffs if nothing can be done to stem the flow of migrants," the official said, speaking on condition of anonymity. Some Republicans have told the White House not to count on the same level of support within the party that it received earlier this year when Trump declared a national emergency to divert funds to build barriers at the border. Democrats opposed that move. The proposed tariffs have also been criticized by the U.S. Chamber of Commerce and industry groups due to concerns about increased costs for U.S. businesses and consumers of imported Mexican goods from cars and auto parts to beer and fruit. PRESSURE AT THE BORDER U.S. authorities at the southern border with Mexico have faced in recent years an increase in mostly Central American families and unaccompanied minors seeking asylum to escape criminal violence in their home countries. Mexican Foreign Secretary Marcelo Ebrard will attend the talks on tariffs and immigration, set to take place in Washington at 3 p.m. (1900 GMT) on Wednesday. Ebrard has said the threatened tariffs would be devastating to Mexico's economy and would not stop the waves of migrants from crossing the U.S. border. The Mexican delegation is expected to try to show the White House that authorities are taking steps to stem the flow of migrants, with Mexico detaining double the number each day than it was a year ago. But leftist Lopez Obrador has said he wants to persuade Washington to help tackle the causes of migration by investing in Central America to create jobs and speed up economic development. Mexico's peso rose 0.2% on Wednesday ahead of the meeting on hopes of a resolution to the U.S.-Mexican trade friction. The Mexican economy will likely slip into recession this year if Trump follows through on his tariff threat, a Reuters poll of market analysts showed. As a proportion of Mexico's total U.S. exports in 2018 - $347 billion, according to U.S. data - a 5% tariff implies costs of roughly $1 billion between June 10 and 30. If the tariffs rise further, that cost, too, would surge. An industry source who has met with the Mexican delegation said that ideas being floated to solve the dispute are more border controls and joint security exercises on Mexico's southern border with Guatemala, which Central American migrants pass through on their way to the United States. "It is a resource issue at the end of the day in part and it is also a sovereignty issue for the Mexicans, how much they are prepared to let the Americans come in and manage some of these border issues with them," the source said. The tariff threat has also raised questions over the future of a three-way deal with Canada to replace the North American Free Trade Agreement. U.S. House of Representatives Speaker Nancy Pelosi said Democratic lawmakers have made clear to Mexican officials they wanted to move forward with the new trade pact. "The meeting that we had was very respectful, made clear that we're trying to go to 'yes' on U.S., Mexico, Canada trade agreement," Pelosi, the top Democrat in the U.S. Congress, told reporters of the lawmakers' meeting with Mexican representatives on Tuesday. Reuters