WASHINGTON -- President Barack Obama left little doubt Wednesday that his administration will challenge Arizona's divisive new immigration law, saying the measure "has the potential of being applied in a discriminatory fashion."

After a private meeting with Mexican President Felipe Calderon in the Oval Office, Obama denounced the state law cracking down on illegal immigration and also sent a clear message that a review led by Justice Department lawyers is likely to culminate in legal action.

Obama said that "a fair reading of the language of the statute" suggests that those who appear to be illegal immigrants could be "harassed or arrested."

"In the United States of America, no law-abiding person -- be they an American citizen, a legal immigrant, or a visitor or tourist from Mexico -- should (ever) be subject to suspicion simply because of what they look like," Obama said.

Mexico is deeply unhappy over the Arizona law, which makes it a crime for immigrants not to carry registration papers. Mexican officials went so far as to issue a travel advisory that warns residents that they could face harassment should they visit the state.

Calderon used the news conference to make known his displeasure. Speaking through a translator, he called the law discriminatory, adding that he opposes steps that "criminalize migration."

Calderon is in Washington for two days of high-level meetings and a formal state dinner, the second of the Obama presidency.

At the news conference, the White House permitted only two questions. At the end, as the two presidents walked back into the White House, one reporter shouted a question, asking Obama when he would hold a full-fledged news conference.

There was no response.

Obama offered cautious support for an immigration overhaul that would provide a path to legal status for the estimated 11 million people living here illegally. He gave no deadline for completion of a bill.

Obama said that during his conversation with Calderon, "I reaffirmed my deep commitment to working with Congress in a bipartisan way to pass comprehensive immigration reform."

At present, Obama said he doesn't have commitments of support from 60 senators, the margin needed to defeat a filibuster. He indicated that his problem is with the Republicans, but Democrats are by no means united in wanting an immigration measure passed.

Sen. Ben Nelson, D-Neb., wants U.S. borders to be strengthened before taking up an overhaul bill, a spokesman said. Nelson said last week that comprehensive immigration reform is "a very hard sell until the border is secure."