Former New York City Mayor Rudy Giuliani claimed Tuesday that he turned down two offers from Donald Trump Donald John TrumpBiden on Trump's refusal to commit to peaceful transfer of power: 'What country are we in?' Romney: 'Unthinkable and unacceptable' to not commit to peaceful transition of power Two Louisville police officers shot amid Breonna Taylor grand jury protests MORE to serve in his administration.

Giuliani, who emerged as an ardent Trump supporter during the campaign, told CNN's Chris Cuomo that he was offered two "very high" positions that he turned down.

"It was my own decision not to do it, largely because of my personal life," he said.

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Giuliani wouldn't go into details, but said the positions were "Cabinet-level" and acknowledged that he wasn't offered the position of secretary of State.

Giuliani announced Friday that he had taken himself out of running for the State job, after reports circulated that Trump had told him he wouldn't get the position. Trump named Exxon Mobil CEO Rex Tillerson as his secretary of State pick Tuesday morning.

Giuliani said Tuesday he took himself out of consideration for State so he could focus on his consulting business.

"If I thought I was necessary, I would have stayed in," Giuliani said.