"There is one page in the Trump White House crisis-management playbook, and that is simply to tweet or say something outrageous to distract from a scandal, and the bigger the scandal, the more outrageous the tweet," Earnest said on "This Week" on Sunday.
Trump made the claim about a wiretap in a series of tweets Saturday morning.
Earnest said, "This may come as a surprise to the current occupant of the Oval Office, but the president of the United States does not have the authority to unilaterally order the wiretapping of an American citizen."
"Even when I was in government, I was not in a position of being regularly briefed on an FBI counterintelligence investigation. No one at the White House, including the president of the United States, should be in a position in which they are trying to influence or dictate how that investigation is being conducted," Earnest said.
He added, "The president was not giving marching orders to the FBI about how to conduct their investigations."
Asked by Raddatz about a story last week in The New York Times saying the Obama administration scrambled to preserve intelligence on Russia's alleged interference in the 2016 election, Earnest said he didn't speak to the journalist who penned the story.
"It was important for people to understand exactly what Russia did to interfere in this election, and it was important for the president-elect's team to understand what they were going to confront in office," said Earnest.
When Raddatz asked if he is "concerned the current administration is trying to quash the investigation or even destroy evidence," he said Trump is trying to "distract" attention from his associates' conversations with or ties to Russia.