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 nations' 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 drugs-related crimes.
Mexico also announced on Wednesday that it had detained an alleged drugs cartel member on its list of 24 "most wanted", two days after it offered $2m each for the capture of the men.
Hector Huerta Rios was captured on Tuesday in the northern industrial Mexican city of Monterrey.
Napolitano told the senate homeland security and governmental affairs committee that the US had its own responsibility to halt the flow of guns into Mexico.
Investigators say that nine out of 10 guns retrieved from crime scenes in Mexico are traced back to US gun dealers and US politicians have grown increasingly concerned over the prospect of violence spilling into US cities.
However Napolitano, who is due to visit Mexico herself next week along with Eric Holder, the US attorney general, said that she could "not discount" a possible rise in violence as the US moved to increase its participation in the fight against the cartels.
An increase in drugs-related kidnappings has already been noted in some US cities, US authorities say.
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 (ATF) are to be sent to the US-Mexico border within 45 days to crack down on the flow of arms from the US into Mexico.
The US will also use part of the $700m that US congress has appropriated for the 2008 and 2009 financial years to provide aid to Mexican law enforcement and military - including five helicopters.
Mexico praised the move, with Espinosa saying it was "consistent with the bilateral co-operation in the fight against organised crime".
More than 1,000 people have died in Mexico this year as drugs cartels battle for lucrative drug-smuggling routes into the US.
Calderon declared tough action against the country's drugs 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 on the crisis.