"I think we need a special counsel to investigate the Fusion GPS episode between the Democratic Party, Mr. Steele and Russian operatives," Graham told "Fox News Sunday," regarding the memorandum written by former British spy Christopher Steele and partly financed by the Democratic National Committee and the Hillary Clinton campaign, which allegedly outlines how the Kremlin obtained material that could be used to blackmail President Trump.
"I think we need a special counsel to investigate the Uranium One episode where thousands of dollars were given to the Clinton Global Fund and former President Bill Clinton from groups tied to Russia," Graham continued, referring to the 2010 deal approved by the Obama administration that allowed a Russian nuclear energy agency to gain a financial interest in U.S. uranium production.
But Graham said Trump "crossed a line" by calling on the Department of Justice and the FBI to look further into the Clintons.
"The president of the United States is in charge of the executive branch," Graham said. "It's not his job to be telling the attorney general to prosecute a particular individual or group."
Graham also called on the Justice and Defense Departments to better coordinate how to hold and handle terror suspects, saying the agencies were "woefully unprepared" for the New York City terrorist attack on Tuesday.
"I wanted to hold him for a long period time, let our military, CIA interrogate him about what he knows about terrorism, how he got radicalized," Graham said of suspect Sayfullo Saipov, adding that now the 29-year-old Uzbek had a lawyer it would be more difficult to extract intelligence.
Saipov is accused of killing eight people and injured almost a dozen more when he drove a Home Depot truck into a bicycle path in lower Manhattan on Oct. 31.
Graham said he thought "the president has right [the] attitude for fighting the war on terror ... but clearly the Trump administration is doing exactly what Obama administration did" by not naming Saipov an enemy combatant.