The vandalism was committed on four tombstones in a predominantly Muslim area of the Newport graveyard.
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A swastika was one of the symbols daubed on a Muslim grave in the Newport cemetery
A council graffiti team is still working to remove the marks - which have left the local community in shock.
Mubarak Ali, who is secretary of the Islamic Society for Wales, urged the Muslim community to remain calm, despite the grave of his relative Sardar Ali being damaged.
"I'm appealing to the Muslim community for calm and not to react in a negative or violent way to this evil incident. Obviously, people are really angry and upset, but we must remember it is a small minority of idiots who did this.
"Most people in Newport get on very well, from all different backgrounds and it's only the small minority that spoils it for the others," the 51-year-old said.
Further graffiti mentioning murdered soldier Lee Rigby and Allah
Ali, who had been planning a vigil for murdered soldier Rigby, added: "What happened to Lee Rigby was evil, wicked. It was caused by extremists - they don't represent the mainstream or vast majority of Muslims.
"Most of us are law-abiding citizens of this country. We respect the Queen, country and armed forces.
"I'm still hoping for the candlelit vigil for Lee Rigby and collection for Help for Heroes to go ahead soon in Newport."
The attackers also targeted the grave of Tariq Hussain, who died of a heart attack at the age of 39 in January 2012.
His younger brother, Shakeel Hussain, 33, said: "When I first heard of it, I was just shocked. They are deceased - it is such a shameful act."
David Phillips, chief executive of South East Wales Equality Council (SEWREC), condemned the actions.
He said: "I think most of the people of Newport would share my views in saying that it's a disgraceful act.
"But it is very misguided as well. The people at the graves and their families were not responsible for Lee Rigby's death and in that sense, it's an own goal."
A Gwent police spokesman told the Huffington Post UK: "The investigation is ongoing. At about 8.40am on Sunday we received a call reporting graffiti on four separate headstones.
"We can't be sure when it happened or how long it had been there. If you have any information please call Gwent Police on 101 or Crimestoppers on 0800 555 111."