The pope made his appeal in his annual address to the diplomatic corps as tens of thousands of people joined a third day of nationwide demonstrations in Myanmar against the military's removal of elected leader Aung San Suu Kyi a week ago.
In a speech to diplomats from more than 180 countries, Francis spoke of his "affection and closeness" to the people of Myanmar, which he visited in 2017.
"The path to democracy undertaken in recent years was brusquely interrupted by last week’s coup d’état," Francis said.
"This has led to the imprisonment of different political leaders, who I hope will be promptly released as a sign of encouragement for a sincere dialogue aimed at the good of the country," he said.
The speech to diplomats is sometimes called his "State of the World" address because it takes in conflicts and international disputes around the globe.