Peter Greste, Mohamed Fadel Fahmy and Baher Mohamed from Al Jazeera English were arrested by Egyptian authorities on December 29 and have been held since.
Egyptian authorities say the journalists held illegal meetings with the Muslim Brotherhood, which was declared a terrorist group last month.
“Three of my colleagues are in jail for doing their job, as you know well,” Amanpour said.
Sawiris raised doubts about the journalists’ credentials to be in the country, and said that al Jazeera was “fabricating” stories.
“These are allegations that they’ve obviously denied, and we deny it on behalf of our colleagues as well,” Amanpour said.