The 23-year-old Joseph Cassano worked as a fire department EMT, but he resigned the position on Monday as news of the tweets spread.
The New York Post reported that he tweeted a slew of derogatory statements about Jews, blacks and the poor.
Cassano issued a statement early Monday saying he regretted "posting some comments that were offensive, especially since I enjoy my job and treat every patient with great care and respect."
His father, FDNY Commissioner Salvatore Cassano, issued a written statement.
"I am extremely disappointed in the comments posted online by my son Joseph, which do not reflect the values - including a respect for all people - that are held by me, my family and the FDNY," he wrote. "There is no place - and I have no tolerance - for statements that would harm the good reputation we enjoy due to our honorable service to all New Yorkers."
The commissioner said he believed that his son made the right decision by resigning and apologizing.