The graffiti on the building in Sutton in South Londonwas spray-painted from the site of the attack, which is more than 19 km away.
The Islamic Centre has no connection to the attackers who carried out the terror attack on Saturday night, the metro.Co.Uk reported.
But the building's very presence has provoked the ire of racists and Islamophobes in the area, it said.
"I am appalled and angered by the terrorist attacks at London Bridge and Borough Market, in my home city. These acts of violence were truly shocking and I condemn them in the strongest terms," he said.
"Muslims everywhere are outraged and disgusted at these cowards who once again have destroyed the lives of our fellow Britons," Khan added.
"That this should happen in this month of Ramadan, when many Muslims were praying and fasting only goes to show that these people respect neither life nor faith. My prayers are with the victims and all those affected. I commend the work of our emergency services working hard to keep us safe and cope with the ensuing carnage, he said.
At least 48 people have been injured in the attack, the third to hit Britain in less than three months and just days before the general election on June 8.
The attack comes as British Prime Minister Theresa May blamed the "evil ideology of Islamist extremism".
"We are concerned about some elements of Theresa May's statement earlier today. May acknowledged as Jeremy Corbyn did nine days ago in response to the Manchester attacks, that such attacks are a perversion of Islam not representative of Islam," Sabby Dhalu, Stand up to Racism Co-Convenor, said.
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