"At a time when the Mexican government has so courageously taken on the drug cartels that have plagued both sides of the borders, it is absolutely critical that the United States joins as a full partner in dealing with this issue," Mr Obama said.
He said he preferred to focus on enforcing existing laws to keep US assault weapons out of Mexico, rather than trying to renew a US ban which expired in 1994.
Backtracking on a campaign pledge to reinstate the ban, Mr Obama said that doing so would be politically difficult.
The Mexican leader hailed a "new era" where Mexico and the US faced challenges together.
Aside from combating the drug menace, Mr Calderon said the two leaders had agreed on a new framework on clean energy and climate change that set out a legal framework and bilateral market mechanisms for carbon emissions.
He said proposals to reduce greenhouse gas emissions would also be discussed.
Mexico is Mr Obama's only stop on the way to the Summit of the Americas, being held in Trinidad and Tobago.
For most Mexicans, the main concern is reviving the economy, says the BBC's Stephen Gibbs in Mexico City.
Mexico sends 80% of its exports to the US and millions of Mexican families rely on remittances from relatives working north of the border, our correspondent says.
Relations between the US and Mexico hit a low point earlier this year when a US military report said drugs-related violence was in danger of turning Mexico into a failed state.
Over the past two years, some 8,000 people have been killed as gangs battle for control of the lucrative drug trafficking routes into the US.
But President Obama's administration has since expressed solidarity with Mr Calderon who has sent hundreds of troops to regain control of the worst-affected areas.
During a visit to Mexico City in March, US Secretary of State Hillary Clinton said that the US shared responsibility for the drugs problem.
She said America's "insatiable demand" for illegal drugs fuelled the trade and that the US had an "inability" to stop weapons from being smuggled south.
Mr Obama has sent hundreds of federal agents along with high-tech surveillance equipment and drug-sniffer dogs to help Mexico fight the cartels.
On Wednesday, the US placed three Mexican organisations on its list of suspected drug syndicates and Mr Obama also charged a senior official with stopping drugs-related violence crossing from Mexico into the US.
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