Sen. Christoper Coons (D-Del.) in an interview Sunday called President Trump's claims that former President Barack Obama Barack Hussein ObamaGOP senator blocks Schumer resolution aimed at Biden probe as tensions run high D-Day for Trump: September 29 Obama says making a voting plan is part of 'how to quarantine successfully' MORE wiretapped Trump Tower before Election Day "remarkable."

"These are remarkable allegations, I think another attempt by President Trump to change the subject," Coons said on "Fox News Sunday."

"But this deserves full investigation. And the larger point I think, that I will agree with Sen. [Tom] Cotton (R-Ark.) on, is that it's in the best interest of our country for us to move forward promptly and get to the bottom of this."

Coons said he believes no president should ever "directly order an intercept or wiretap on an American citizen."

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"That's not what our system provides. You have to go in front of a judge and get a warrant in order to conduct a wiretap," he said.

Coons said one of two scenarios likely occurred.

"Either President Trump has inappropriately released classified information and was himself the subject of a court-ordered wiretap," Coons said.

"Or, and I think this is a very remote possibility, there was some inappropriate actions by the previous administration."

Either way, Coons said it doesn't help the country "for this to all be worked out on Twitter."

"It ought to be worked out in a full, fair, prompt and thorough investigation, whether by the Senate Intelligence Committee, if they can get to the bottom of this," he said. "Or by a special prosecutor."

Coons added that it's possible President Trump's claims just aren't true, adding that the president offered "no evidence or backing for his outlandish claims."

The president on Saturday claimed Obama had his "wires tapped" in Trump Tower before his presidential victory. He laid out the claims without any evidence and questioned whether it was legal for a sitting president to be "'wire tapping' a race for president prior to an election."