"Despite their enormous contribution to the economy and society of the United States," Calderon said, millions of immigrants "still live in the shadows, and at times, like in Arizona, even face patterns of discrimination".
Obama has also opposed the Arizona law.
'Uniting our people'
Calderon said that the two nations needed to work together to provide a resolution to the sensitive immigration issue.
"We can do so if we create a safer border, a border that will unite us instead of dividing us, uniting our people," he said.
"We can do so with a community that will promote a dignified life in an orderly way for both our countries."
Patty Culhane, Al Jazeera's correspondent in Washington, said: "It is unusual for Calderon to speak out at the start of the visit.
"Considering that Obama stuck to niceties, so to get into policy is a little bit unusual.
"But we do know Calderon is outraged by this law."
She said that the new law was very controversial in the US, but opposing it could be problematic for Obama.
"Obama has asked the justice department to look into it," our correspondent said.
"But he is walking a political tightrope as, although there have been protests in certain cities against it, if you look at public opinion, it is not against this law."
The Arizona law requires immigrants to carry papers proving their right to residency and allows the police to question anyone they suspect of being in the country illegally.
Many critics say the law is an excuse for racial profiling.
Arizona officials have denied the accusations, saying that the law forbids racial profiling.
Supporters have said that the law is needed to curb crime in the desert state, which is home to an estimated 460,000 illegal immigrants and is used by drug and people traffickers operating from Mexico.
Obama, who was to host a formal state dinner for Calderon later on Wednesday, was also expected to discuss drug violence on the two nations' mutual border.
War on drugs
More than 22,700 people have been killed in Mexico since December 2006, when Calderon initiated a large military offensive against drug traffickers.
Washington has provided financing, training and equipment for the fight as part of a $1.3bn initiative, and has stated that US demand for drugs is a major factor in the problem.
Climate change, economic issues and access of Mexican truckers into the US are also thought to be on the agenda for talks.
Our correspondent said that more money is expected to be made available by the US to stop the drug trade, and that Obama has pledged to try to end demand for drugs in the US.
Calderon is due to speak at a joint session of the US congress during his visit.