Joshua, dubbed "The Prophet" by fanatical followers because of his purported predictions and healing powers, showed footage of the moments leading up to the collapse on his emmanuel.Tv network.
Nigeria's National Emergency Management Agency (NEMA) said 42 people were killed in Friday's incident, while 130 escaped or were pulled out alive from the rubble.
In the security camera footage, apparently from opposite the vast church compound, what is described as an aircraft is seen over the building four times at 11:30 am (1030 GMT), 11:43 am, 11:45 and 11:54 am.
"After the incident, the strange aircraft does not return," a commentary accompanying the images adds.
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There was no independent verification of the authenticity of the footage but Joshua has said he would make it available to Nigeria's security agencies.
His Synagogue Church of All Nations (SCOAN) is located in Ikotun, near Lagos international airport.
Joshua's theory about the low-flying plane featured in a number of Nigerian newspapers today.
But NEMA's southwest coordinator Ibrahim Farinloye rejected claims of sabotage and said extra floors were being added to the building without changing the foundations.
Building collapses are common in Nigeria because of the use of sub-standard material and flouting of construction regulations.
NEMA rescue workers were only able to access the site properly at 9:00 am today and the emergency services and media had previously complained of being attacked by church security.
The Lagos state building control agency also complained that its officials were obstructed and Farinloye indicated more lives could have been saved had rescuers been able to get to the building sooner.