Story highlights Vulnerable Republican Sen. Mark Kirk said he cannot support his party's presumptive nominee

Kirk criticized Donald Trump's comments regarding an American judge of Mexican descent

Washington (CNN) Republican Sen. Mark Kirk said Tuesday that Donald Trump "does not have the temperament" to hold the job of president, saying he "cannot and will not support" the presumptive GOP presidential nominee.

It was sharp criticism from an incumbent who had previously insisted he would support the GOP nominee.

The Illinois Republican, who faces a tough challenge this November from Illinois Democratic Rep. Tammy Duckworth, tweeted Tuesday that based on his background in the military, he does not have faith in Trump to lead.

"Given my military experience, Donald Trump does not have the temperament to command our military or our nuclear arsenal," Kirk wrote.

Given my military experience, Donald Trump does not have the temperament to command our military or our nuclear arsenal. — Mark Kirk (@MarkKirk) June 7, 2016

Kirk, who told CNN that he would write in former CIA director David Petraeus this fall, followed up with a statement saying he objects to Trump's recent comments about a federal judge's Mexican heritage.

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