MONTERREY, Mexico (Reuters) - U.S. Secretary of State Hillary Clinton placed a bouquet of white roses at a basilica and watched police storm an airplane in a mock hostage rescue as she ended a two-day visit to Mexico on Thursday.

The incongruous images illustrated the complexity of the relationship between the United States and Mexico, countries bound by many cultural and family ties but also by the illegal drug trade and its deadly violence.

In a series of appearances on her two-day trip, Clinton tried to paint the U.S.-Mexican relationship in more subtle shades than the stark headlines about gangland murders and turf wars among drug traffickers that dominate the news headlines.

Mexico is facing brutal violence between rival drug gangs and the army in a battle that killed 6,300 people last year.

Clinton began her day at Mexico City's Basilica of our Lady of Guadalupe, a vast circular church built in the 1970s near the site where the Virgin Mary is believed to have appeared before an indigenous peasant, Juan Diego Cuauhtlatoatzin, in the 16th century.

Clinton placed a bouquet of white roses near the altar where Juan Diego's apron is displayed in the church, which has a moving sidewalk to help the millions of faithful who visit each year.

An hour later, she stood on the flatbed of a police truck at a sprawling police base in Mexico City's rough Iztapalapa neighborhood where she saw helicopters, bomb-sniffing dogs and scores of police recruits.

She then watched two dozen masked, black-clad police officers creep up to an airplane, scale it with metal ladders and punch in its doors in a simulated hostage rescue aimed at showing her Mexican police training.

"These two days have cast in sharp relief the breadth and depth of the U.S.-Mexico relationship," Clinton told a news conference in the northern city of Monterrey.

Clinton ended her day in Monterrey, a prosperous manufacturing and services city close to the U.S. border that has seen a spike in drug violence over the past six months.

Speaking to students at the city's TecMilenio University, Clinton said the United States would work with Mexico to address the drug trafficking "that has terrorized Mexican communities, especially those along the border.

"This situation is intolerable," she said.

"We have to have better surveillance along our border going both ways," she added. "We should worry about what is coming north but the Mexican people are worried about what's coming south: assault weapons, bazookas, grenades."

By Arshad Mohammed, Reuters, March 26, 2009