Gandhi had posted his resignation letter on microblogging site Twitter on Wednesday.
Priyanka retweeted her brother's letter with a message.
"Few have the courage that you do @rahulgandhi. Deepest respect for your decision," she said.
In the four-page open letter, Gandhi had urged the Congress Working Committee (CWC) to entrust a group of people with the task of finding a new president as it would not be proper for him to do so.
The 49-year-old also stressed on the need for the Congress to "radically transform itself".