(Reuters) - A day after his confrontational election-year State of the Union address, President Barack Obama had a tense exchange with Arizona's Republican governor Wednesday as she greeted Air Force One in Phoenix.

During their brief encounter on the tarmac, intended to be a ceremonial welcome, Obama told Gov. Jan Brewer that he disagreed with an account she had given of a meeting they had at the White House two years ago.

He was a little disturbed about my book, 'Scorpions for Breakfast,' Brewer told reporters after the conversation. At one point during their chat, she pointed a finger at the president.

Brewer, who has differed with Obama over immigration, handed him a letter asking him for a meeting to talk about Arizona's economy when she greeted him. A White House official said the subject of the book came up after Brewer gave Obama the letter.

The president said he'd be glad to meet with her again, but did note that after their last meeting, a cordial discussion in the Oval Office, the governor inaccurately described the meeting in her book. The president looks forward to continuing taking steps to help Arizona's economy grow, the official said.

Brewer's book is about a rancher killed near the U.S.-Mexico border.

In 2010 she signed a controversial bill cracking down on illegal immigrants in Arizona that called for police to check the immigration status of anyone suspected of being in the country illegally.

The president visited Arizona as part of a three-day, five-state tour following his State of the Union address.

In that Tuesday night speech, he blamed Republicans for getting in the way of measures to recover from crisis and mentioned comprehensive immigration reform as one of his priorities as the November election nears.

Obama has referred to the Arizona immigration law as misguided. Critics have said the measure is a mandate for racial profiling, but its supporters believe tougher measures are needed to prevent non-citizens from taking U.S. jobs in a tough economic climate.

(Editing by Xavier Briand)