President Obama and Arizona Gov. Jan Brewer had a tense exchange on an airport tarmac on Wednesday afternoon after Air Force Once landed near Phoenix.

Obama, who was in the area for a speech, is often warmly greeted by elected officials when he lands. Brewer, who in 2010 signed a controversial immigration law the president has opposed, gave Obama a handwritten letter inviting him to have lunch with her and visit the Arizona-Mexico border.

The president in turn, according to a White House official, “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.”

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The pictures of the scene illustrated more than the words. Brewer pointed her finger at Obama, while the president appeared to walk away in the middle of the conversation.

Brewer told reporters later Obama “was a little disturbed about my book.”

She later added, “I felt a little bit threatened, if you will, in the attitude that he had, because I was there to welcome him.”

As she describes in her new book Scorpions at Breakfast, Brewer believes the president lectured her at the White House in 2010 when the pair met about the Arizona immigration law, which gives the police in the state broad power to detain anyone who is suspected of being an illegal immigrant.

The White House disputes her account, which Obama told Brewer personally on the tarmac.

The encounter is likely to raise concerns among some liberals, who say Republicans not only oppose the president’s policies but show a lack of respect for him personally. But former House Speaker Newt Gingrich slammed Obama as unwilling to take criticism in an interview on FOX after the encounter.

Follow Perry Bacon Jr. on Twitter at @perrybaconjr