''There's no secret that al-Qaida will try to get into this country and into other countries by any means that they possibly can,'' Rice told reporters. ''That's how they managed to do it before, and they will do everything that they can to cross borders.''

The top U.S. diplomat met with Mexican President Vicente Fox and Foreign Affairs Secretary Luis Ernesto Derbez in high-level talks that focused heavily on border security, immigration and improving economic ties between the United States and Mexico.

Rice announced a $10 million grant to help nurture development of small businesses in Mexico, particularly those involving women, and joined Mexican officials in resolving a lingering water dispute between Mexico and South Texas farmers. Mexico agreed to repay most - but not all - of Rio Grande water owed to Texas under a 1944 treaty.

The daylong trip was Rice's first visit to Mexico since becoming secretary of state five weeks ago.

In testimony before Congress last month, Adm. James Loy, who at the time was deputy secretary of Homeland Security, said intelligence strongly suggested that ''al-Qaida has considered using the southwest border to infiltrate the United States,'' possibly with the help of criminal gangs operating along the border.

Rice confirmed that U.S. officials ''have from time to time had reports about al-Qaida trying to use our southern border,'' as well as the northern border with Canada.

Estimates of immigrants crossing the Mexican border each year into the United States range from hundreds of thousands to millions.

Increasingly they transit Mexico from other countries, and often elude outnumbered border patrolmen.

Rice said that border security will be a top priority of new Homeland Security chief Michael Chertoff and will be high on the agenda of a summit of President Bush, Fox and Canadian Prime Minister Paul Martin March 23 at Bush's ranch in Crawford, Texas.

Rice displayed little patience with American citizens in Texas, Arizona and other border states who have organized into patrols to prevent illegal immigration.

''From our point of view, the U.S. government is not supporting these activities,'' Rice said. ''You can be certain if there are any laws broken, that people are going to be held accountable.''

Rice, conducting her first one-on-one meeting with the Mexican president, met with Fox at Los Pinos, the equivalent of Mexico's White House.