Hollande spoke in the wake of a scandal that has forced his budget minister, Jerome Cahuzac, to resign, Radio France Internationale reported.
Cahuzac, who has been charged with tax evasion amid revelations he was using a numbered Swiss bank account, has threatened to cause a wider scandal that would spread to conservative politicians.
Critics have said leaders of the Union for a Popular Movement, the conservative party of former President Nicolas Sarkozy, knew about Cahuzac's financial irregularities several years ago and did nothing.
Hollande made his statement during a visit to Tulle, the southwestern town where he was once mayor.
"At a time when there are values that must be upheld, moral requirements that apply to everyone who has any responsibility at any level, everyone must serve the republic and in an exemplary fashion," he said.
Notable deaths of 2014 [PHOTOS]