"The criminals and kingpins spreading violence are trying to corrode the foundations of law, order, friendship and trust between us. They will fail," Clinton said in Mexico City.
The US secretary state, on her first trip to Mexico since taking up the post, also said the US would provide $80m to the Mexican government to buy Blackhawk helicopters to combat the cartels.
"These aircraft will help Mexican police respond aggressively and successfully to the threats coming from the cartels," Clinton said.
More than 1,000 people have died in Mexico this year as drug cartels battle for lucrative drug-smuggling routes into the US.
Clinton also admitted some US responsibility for the smuggling of arms by the cartels from the US into Mexico.
"Our inability to prevent weapons from being illegally smuggled across the border to arm these criminals causes the deaths of police officers, soldiers and civilians," the chief US diplomat said.
"So yes, I feel very strongly we have a co-responsibility, and part of what we are trying to do is not only acknowledge that but working with the Mexicans to create the very best possible responses."
|Hector Rios was arrested after Mexico offered $2m for each man on a "wanted" list [AFP]
The US secretary of state's visit comes a day after the US unveiled its new strategy to tackle violence from Mexico's drug cartels, including the deployment of extra US federal agents at the violence-plagued border.
It also comes as Janet Napolitano, the US homeland security secretary, told congress on Wednesday that the US could see a rise in drug-related crimes.
Mexico also announced on Wednesday that it had detained an alleged drug cartel member on its list of 24 "most wanted", two days after it offered $2m for the capture of each man.
Hector Huerta Rios was captured on Tuesday in the northern industrial Mexican city of Monterrey.
On Tuesday, Napolitano also revealed US plans to boost the number of agents from the US departments of justice, treasury and homeland security for border security and to station new inspection technology at border stations.
About 100 agents from the bureau of Alcohol, Tobacco and Firearms are to be sent to the border within 45 days to crack down on the flow of arms from the US into Mexico.
The US will also use part of $700m that the US congress has appropriated for the 2008 and 2009 financial years to provide aid to Mexican law enforcement and the military.
Mexico praised the move, with Espinosa saying it was "consistent with the bilateral co-operation in the fight against organised crime".
Calderon declared war against the country's drug gangs shortly after entering office in 2006, sending thousands of troops to the border, a move which sparked an explosion of violence from the cartels.
Calderon is due to hold talks with Barack Obama, the US president, on April 16 and 17 in Mexico.