But Obama, who has said the US bears some responsibility for the drug trafficking problem, also expressed "the importance of human rights for him, for the United States and frankly for Mexico" in the battle against the cartels, the official said.
Human rights groups and US politicians have raised concerns about alleged abuses by Mexican soldiers during the military crackdown on the gangs.
Just hours before the talks a commando shot dead a lawyer known for her work defending suspected drug smugglers in the north of the country.
The Mexican presidency said the two presidents agreed to "continue boosting joint co-operation against organised crime on both sides of the border, based on ... respect for the legal framework of each country".
But Calderon also raised the issue of delays in delivery of part of a $1.4bn US security aid package known as the Merida Initiative.
Meanwhile, Canada announced that it would increase training by its federal Mounted Police for Mexican officers as part of a $15m a year security programme for the Americas.
"Supporting police training in Mexico is one of the most effective ways to fight organised crime and drug trafficking within Canada," a statement from Harper's office said.Lorry dispute
The leaders' meeting on Monday was also expected to focus on trade ties, as well as controversial trade restrictions that prompted protests ahead of the summit.
Obama has stressed the need for a new tone in the US-Mexico relationship, but his administration made little progress on divisions between the two over a ban on Mexican lorries travelling north of the shared border.
During Sunday's meeting, Calderon reportedly questioned Obama over an earlier pledge to restore the cancelled programme, which allowed goods from Mexico to be taken to their destinations in the US by the Mexican driver.
The US move violated the North American Free Trade Agreement (Nafta) and Mexico's retaliation sparked anger among US companies, which have urged an end to the dispute.
Trade relations between the US and Mexico have been strained since Mexico placed about $2.4bn in tariffs on 89 US products following Washington's decision to cancel the the lorry programme.