Protesters burned US flags and threw stones at police guarding the building.
Tear gas was used to disperse the crowds. Several people were injured, including a number of police officers.
The violence came hours after Mr Bush pledged to reform controversial immigration laws, during two-day talks with Mexican President Felipe Calderon.
The US president has visited Brazil, Uruguay, Colombia and Guatemala. Mexico is the final stop on his seven-day tour of the region.
Several protesters were arrested or injured, one with blood pouring from his head, as they dispersed.
Guadalupe Fernandez, 64, who was protesting but not involved in the violence, said they were "in disagreement with the war policy" of Bush.
He said: "Bush is desperate because
Lorenzo Fernandez, the commanding officer at the scene, said the police were only defending themselves.
The officer said: "These are people who don't know how to demonstrate pacifically."
In the city of
About 30 protesters also ran into
During the tour, leaders of
Police arrested demonstrators in
Merida and Mexico City [Reuters]
It was a topic likely to come up again in talks on Wednesday between Bush and
As long as the
Calderon took over in December from Vicente Fox, who failed to get an immigration deal with Bush during his term.
Bush is pledging to push the Democratic-led US Congress to complete action on immigration this year with significant steps taken by August, before the campaign for the 2008 race to succeed him completely takes over.