The exchange happened as Trump met in the White House with sheriffs from counties around the country, to defend his controversial travel ban.
"Asked at Tuesday's White House briefing if Trump would accept the court's ruling, Spicer said that the president will respect the ruling, but also voiced confidence that the administration will "prevail ... on the merits of the case".
The 78 incidents include two un-covered terrorist attacks in Saudi Arabia, including the one that left a Danish citizen injured in November 2014 and the other, which left two Americans Dead in January 2015.
He didn't give examples of any attacks that weren't being reported by the press.
"But you can't ignore the terrible violence we're seeing in our major cities", he insisted. Look at The New York Times, which the President demonizes often. Reporters, he said, intentionally hide news of terrorist attacks from the public, ostensibly to minimize the kinds of national security threats he says back up his refugees and citizens of seven Muslim countries from entering the United States.
"There's no question the president respects the judicial branch and its ruling", Spicer said.
"Other programs as well as CNN International covered most if not all of them, majority exhaustively", Cooper added.
"Radical Islamic terrorists are determined to strike our homeland as they did on 9/11, as they did from Boston Orlando to San Bernardino and all across Europe", he said.
He added: "To be sure, we as a program did not cover each and every incident on the list, however other programs, as well as CNN International covered most if not all of them, many of them exhaustively". He said the White House would issue a list of underreported terror attacks to substantiate Trump's claim. The two others got a single mention each - a knife attack that wounded a US citizen in Pakistan in 2015 and a suicide bombing that killed 14 Nepalese security guards in Afghanistan past year.