Vicente Carrillo Leyva, alleged senior leader of the Juarez cartel, held in the capital.
“You can’t fight this war with just one hand,” he said.
“You can’t have Mexico making an effort and the United States not making an effort.”
Last month, Hillary Clinton, the US secretary of state, admitted that US demand for illegal drugs and its inability to halt weapons smuggling into Mexico had contributed to violence which had left almost 7,000 dead since early 2008.
Obama and Calderon also discussed the economic crisis, trade, green energy and immigration before they were set to travel to Trinidad and Tobago for the Summit of the Americas, beginning on Friday.
The US government has announced a number of initiatives in recent weeks aimed at helping ease the violence from drug gangs fighting each other for control of lucrative cross-border trade routes.
The White House plans to tighten controls at the US-Mexico border to halt weapons-trafficking to Mexican cartels and is hoping to send Black Hawk helicopters to help Calderon defeat the drug gangs.
Mexican officials also want the White House to reinstate a ban, which expired in 2004, on assault weapons.
Mexican police estimate that about 90 per cent of weapons used by Mexican gangs, including the Gulf and Sinaloa cartels, come from the US.
On Wednesday, Janet Napolitano, the US homeland security secretary, named Alan Bersin, a former justice department official, as a “border tsar”.
Calderon declared a war against the country’s drug gangs shortly after taking office in 2006, sending thousands of troops to the border, a move which sparked an explosion of violence from the cartels.