Appearing as MC at the International Press Freedom Awards, Smith also announced he would donate $500,000 to the Committee to Protect Journalists.
The sentences show a "further backsliding on rights under Aung San Suu Kyi's government."
Arkady Babchenko has been criticized for handing a victory to pro-Kremlin media.
There were 259 journalists in jail by the end of 2016, according to the Committee to Protect Journalists.
According to three organizations, no real evidence of Martinović's involvement with criminal activity has been presented.
The number of jailed journalists in Turkey has doubled in a year.
The Committee to Protect Journalists released its annual report Tuesday.
In 2014, 220 journalists were imprisoned worldwide, the second worst year on record, the Committee for the Protection of Journalists reports.