North America's three top leaders sat down for one-on-one talks on border security, illegal immigration and terrorism, and were attending a dinner hosted by Mexican President Vicente Fox late Thursday.

On Friday, they will join together for a trilateral meeting before President Bush returns to the United States.

The two-day summit among Canada, the U.S. and Mexico is aimed at tightening border security. The U.S. president was prepared to discuss terrorist threats to the United States that come by land, but the other leaders have their own issues to bring up.

The summit started off Thursday with a cordial visit to Mayan ruins.

"This is a good start to a very important series of discussions," Bush said at Chichen-Itza, a sacred Mayan site in the Yucatan state. "We've got vital relations that matter to the future of our people."

Bush, who wore a cream-colored Hawaiian shirt, traveled to the archaeological ruins by helicopter with Canadian Prime Minister Stephen Harper, who took office two months ago as Canada's new Conservative leader. Fox met the two leaders at the site.

The three leaders spoke briefly to reporters after the regional director of the country's national institute of anthropology and history detailed different points at the site. The three also heard a traditional band play music, walked around a large plaza and climbed about half a dozen steps of the pyramid at the center of the site.

Harper said the ruins were "a symbol here of our determination to build a new future for all inhabitants of North America."

Fox and Harper's predecessor, Paul Martin, signed the trilateral Security and Prosperity Partnership a year ago near Bush's Crawford, Texas, ranch. The partnership focuses on protecting North America from terrorists and the continent's global competitiveness with China and other countries.

While in Mexico, Harper expressed interest in discussing a dispute over U.S. tariffs on Canadian softwood lumber imports. He said he wants the United States to return billions of dollars in tariffs on the lumber that NAFTA and the WTO courts have ruled were either illegal or excessive.

Bush said he was "always optimistic" they could find a solution to the dispute, though he thought the two sides were "pretty close to a deal a couple years ago."

"It's going to require some very quiet consultations," Bush said in a pre-trip interview.

Other issues important to Canada are other trade matters, Iraq and a U.S. plan to require passports or other identification at entry points of the United States. The United States plans to require passports to cross beginning in 2008. But Canadians say drivers' licenses ought to be enough. The president says those documents are too easily forged.

Mexico hopes to address a migration accord on the status of about 6 million illegal immigrants from Mexico who reside in the United States.

Before leaving Washington, Bush told foreign reporters not to underestimate his ability to broker an immigration legislation compromise with a guest worker program supported by Mexico. Speaking at the ruins, Fox told reporters that it isn't up to him and Bush to come up with a guest worker program, but is in the hands of the U.S. Congress. He said it is important for he and Bush to give as much information as possible to Congress to make decisions.

The meeting was occurring as the Senate took up debate on illegal aliens, an issue that has drawn hundreds of thousands of immigrants to protests in the streets of cities nationwide.

The legislation would strengthen border security, legalize some undocumented workers, establish temporary guest worker programs and allow illegal immigrants currently in the United States to apply for citizenship without first returning home.

Democrats support the legislation, and have won over several Republicans, including some in the Senate Judiciary Committee who approved legislation that makes many concessions to illegals.

But some GOP lawmakers say they worry that a guest worker program would offer a path to citizenship that is too similar to amnesty. These same lawmakers say they'd like Mexican officials to do more on their side of the border to stop illegal immigrants and give U.S. authorities more intelligence about them.

The issue is a big one for Fox, who has staked his reputation on getting some form of legal status for all illegal Mexicans, possibly through a guest worker program. But Fox's term expires in July and he is unable to run again due to term limits. Political observers say a guest worker program being approved before the July elections could help a candidate from his party win office.

FOX News' Wendell Goler and The Associated Press contributed to this report.