Seven people were killed and 48 injured when three terrorists drove into pedestrians on London Bridge before launching a knife rampage on Londoners enjoying a Saturday night out.
The men, wearing fake suicide belts, were shot dead at the scene by armed police within eight minutes.
The Muslim Council of Britain condemned the attack in the strongest terms.
Harun Khan, Secretary General of the Muslim Council of Britain, 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.
"Muslims everywhere are outraged and disgusted at these cowards who once again have destroyed the lives of our fellow Britons.
"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 emergency services working hard to keep us safe and cope with the ensuing carnage.
"As ever we urge everyone to assist the authorities so that these criminals can be apprehended and brought to justice."
Mr Khan wrote online last night: "Shocked and concerned at ongoing developments in #LondonBridge and #BoroughMarket. Prayers for those affected"
Police said Sunday they were working to establish whether everyone was accounted for and paid tribute to Londoners for their response.
Met Commissioner Cressida Dick said the attack was "appalling" and "tragic" in a statement on Sunday morning.