The comments were made at an event in the state of South Carolina on Thursday.
“People accuse me of all kinds of things, but no one accuses me of quitting,” Clinton said in a short speech to supporters in Greensboro, North Carolina. “I’ll never walk away however tough the going gets.”
Clinton suffered what appeared to be a fainting fit and had to be carried by Secret Service officers while attending a memorial gathering for the 15th anniversary of the September 11, 2001 terrorist attacks on the United States on Sunday.
In the days since, opinion polls showed Clinton continuing to fall behind her Republican rival Donald Trump.
Also, reports have circulated that some senior Democratic Party officials are considering how they could replace Clinton with Vice President Joe Biden or another candidate if Clinton’s health worsens.