"If you can't show the American people that international organizations can be more responsible, there is going to be a break [in US financing]. And I am going to lead that break," Graham told CNN in an interview.
He added that he would do the utmost to show where "we [US] stand with the only true democracy in the Middle East, Israel."
On Friday, US President-elect Donald Trump said in a statement that Washington would change its policy toward Israel at the United Nations after he assumes presidency.
Over 500,000 Israeli settlers live in East Jerusalem and the West Bank, which Israel captured during the 1967 war. The settlements are considered illegal by the United Nations.