US President Barack Obama has stressed Washington's support for Mexico's ongoing battle against drug cartels.
A leader of Mexico's powerful Gulf cartel was shot dead on Friday by security forces in a town near the US border.
Ezequiel Cardenas Guillen, known as "Tony Tormenta", was killed in Matamoros, across the border from Brownsville in Texas.
Obama said the US backed Mexico's efforts to end the cartels' "impunity".
"The president offered his condolences to President Calderon on the death of Mexican officials involved in the operation," said a White House statement.
Residents in Matamoros spoke of a shoot-out lasting for several hours.
Cardenas was the brother of former Gulf cartel leader Osiel Cardenas, who was extradited to the US in 2007.
Three suspected gunmen and two marines were also killed in the gun battle, according to federal security spokesman Alejandro Poire. A local journalist died in the crossfire, Mexican media reported.
The day after the shoot-out, gunmen blocked roads in Reynosa, a Gulf cartel stronghold near the US border, and strung up threatening banners.
Meanwhile the Zetas gang, rivals of the Gulf cartel, hung signs between trees and over bridges in Reynosa and in cities across northeastern Tamaulipas state, mocking Cardenas' death.
"Once again, the Gulf traitors' destiny is evident ... there's no place for them, not even in hell," read one banner that was signed by the Zetas, reported Reuters news agency.
Cardenas, 48, had been indicted in the US on drugs charges, and the US Drug Enforcement Administration was offering a reward of up to $5m for his arrest.
He was accused of smuggling tonnes of drugs across the US/Mexico border over the past decade.
Friday's two-hour shoot-out involved 150 Mexican marines, three helicopters and 17 military vehicles.
Local residents were trapped in shops and schools for extended periods and communicated using social networking websites.
"Shelter, everyone! Don't leave your houses please. Pass the word," one resident posted on Twitter.
Bridges across the international border into Texas were closed briefly, as the military used firearms and grenades to tackle suspected cartel members.
The Mexican police and army are struggling to control armed cartels in a number of areas of the country.
Several groups are trying to control lucrative drug smuggling routes into the US.
More than 28,000 people have died in the drugs war since Mexican President Felipe Calderon ordered the army into the fight in 2006.
The policy has had some successes, but that has not led to a decline in the number of killings, or the level of kidnappings, extortion and human trafficking that the gangs also engage in.