Ms O’Neill made her comments after being asked about reports of footage on social media which appeared to show a cavalcade of cars and fireworks being lit in apparent celebration following the Queen’s death.
Some graffiti had also appeared on walls in Londonderry mocking the news.
At the end of the day, she may have been the Queen of England but she was also a mother, a grandmother, I think people should be very respectful
Michelle O'Neill, Sinn Fein
Ms O’Neill said: “This is a time for everybody to be respectful.
“Queen Elizabeth has died, there is a family that is mourning her loss.
“At the end of the day, she may have been the Queen of England but she was also a mother, a grandmother, I think people should be very respectful.
“Queen Elizabeth has died, her family are grieving.”
Asked about jokes about the death of the Queen on social media, Ms O’Neill said: “The British people, people from a unionist identity here are grieving her loss and I think everybody should be very respectful of that and not engage in anything that is anything other than respectful.
“I don’t think its appropriate for anybody to be engaged in any kind of jokey-type behaviour, someone has died and I think it’s important that we are all respectful.”