A bottle is believed to have been thrown towards Mr Khan, who was said to be hiding inside the church as 20 police officers rushed outside to calm the situation.
Photographs showed a man being led away by officers as Metropolitan Police reinforcements headed in, and the atmosphere was said to be 'very tense'.
The man - who has not yet been identified - was allegedly chased by a number of officers, wrestled to the ground and arrested before being taken away.
Mr Khan had been meeting members of the local community at a community centre and was then heckled by children and adults as he spoke to the public live on TV.
In dramatic scenes captured on Sky News, one small boy asked Mr Khan 'how many children died' and 'what are you going to do about it?'
The Mayor said: 'People are justifiably angry and I share their anger and I share their demand for answers.
Mr Khan was meeting members of the local community at a community centre in the area
'Many are grieving and are heartbroken, but also people are frustrated because for years and years they have been expressing their concern, for the last few months more so, and they are justifiably angry, and I share their anger.
'That's why yesterday I said to government ministers that they need to make sure checks are done now to make sure tower blocks are safe. But also we need to make sure that the public inquiry doesn't report in two, three years time.
'We can't afford for that to happen, so what I've said is there will be an interim response this summer to make sure these questions are answered.'
Mr Khan was also said to have been heckled by protesters who felt he has not been supportive of Labour leader Jeremy Corbyn.
Theresa May has ordered a full public inquiry into the fire as emergency services raised the death toll to 17 - with further bodies expected to be found in the flats.
Her demand for the 'terrible tragedy' to be 'properly investigated' echoed calls from London Mayor Sadiq Khan and Mr Corbyn for answers.
Mr Khan said the 'full scale of the tragedy is becoming clear and there are pressing questions, which demand urgent answers'.
The Mayor added: 'That is why I am demanding a full, independent public inquiry into the fire at Grenfell Tower.
'In light of concerns about the safety of other tower blocks that have been similarly refurbished, the inquiry needs to produce an interim report by the end of this summer at the latest.'
The blaze left residents in the 24-storey tower block fleeing for their lives. Mr Corbyn, during a visit to the scene, said the 'truth has got to come out and it will'.
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