"We don't set up walls, and that's not the way you're going to fix this situation," Fox said in Spanish to representatives of groups active in Utah's Mexican community. "It's not with fences that we are going to solve this problem."
There were cheers of "Viva Mexico" as Fox shook hands before leaving for an official dinner at the governor's mansion.
Earlier in the day, at a lunchtime speech to about 500 business, civic and religious leaders, Fox stressed the need for greater cooperation between his country and the U.S. on such issues as trade, energy and security.
Fox discussed his accomplishments during his six-year term, which ends this year, and promoted trade opportunities with Utah and the rest of the United States.
Working together, Mexico and the U.S. can improve the quality of life for citizens in both countries, he said.
"The future of North America must guarantee great competitiveness, greater regional security, greater availability of energy, greater trade exchanges and, naturally, a greater well-being for all of its inhabitants," said Fox, who is also scheduled to visit Washington state and California this week.
He spoke of the steps he has taken to strengthen the Mexican economy and the democratization of his country.
Fox's visit comes as the U.S. Senate considers legislation to strengthen border security, authorize new guest-worker programs and give an eventual chance at citizenship to most of the estimated 12 million people already living illegally in the United States.
Utah, like many states, is divided on immigration. While Utah's largest minority population is Hispanic, there also is growing frustration about the wave of illegal immigrants entering the state.
Jorge Fierro, a Mexican citizen who has lived in Utah since 1986, hopes Fox addresses how he and future leaders can improve the lives of Mexicans. Fierro, who is catering an address Fox is scheduled to make at Rico's Market, opened his first bean stand in 1997 and now sells Mexican food products in supermarkets throughout Utah.
"This is going to boost our morale now that our brothers and sisters are facing uncertainty in their future," Fierro said.
The Minuteman Project, which opposes illegal immigration, is planning protests at the Capitol, where Fox is scheduled to address a special session of the Legislature on Wednesday.
"I'd like to see Vicente Fox tell his people to respect the law and come here legally," said Alex Segura, founder of the Utah Minuteman Project.
About 60 opponents of illegal immigration protested near the governor's mansion before the state dinner, most arguing that Mexico's social problems should be handled by Mexico.
Alvin Lundgren, a member of the Utah Minutemen, said Fox's visit was just "the usual show and no substance."
Fox is to meet privately Wednesday with Gov. Jon Huntsman, a Republican. Huntsman supports President Bush's plan to send as many as 6,000 National Guard troops to the Mexican border and says it's important for Fox to see firsthand the frustrations Western states feel when it comes to illegal immigrants burdening health care and prison systems.
Fox also is expected to meet with leaders of The Church of Jesus Christ of Latter-day Saints. The majority of Utah residents are Mormon, as is the Legislature and Huntsman. The Mormon church also has a strong presence in Mexico, where in 2004 membership exceeded 1 million.
Fox's itinerary in Washington state Wednesday and Thursday includes a meeting with farm workers, a dinner with the governor and breakfast with business leaders.
Later Thursday, Fox is to address a joint session of the California Legislature and meet with Gov. Arnold Schwarzenegger. It will be Schwarzenegger's first meeting with Fox since he became governor in 2003.