The international Christian charity spoke out after producers behind the God's Not Dead franchise announced proposals to make a movie based the dramatic events in Chiang Rai province.
"Before others started thinking about films or future opportunities, we'd want to see the children and families of the children given all of the socio-emotional support that they're going to need...", chief executive for the UK and Ireland Justin Dowds told Premier.
The chief executive and founder of Pure Flix Entertainment, Michel Scott revealed plans to adapt the rescue for the big screen, after he spent several days witnessing the operation first-hand.
He told The Hollywood Reporter: "The bravery and heroism I've witnessed is incredibly inspiring, so, yes, this will be a movie for us."
But Compassion, which enrolled one of the youngsters onto its sponsorship programme, questioned the timing, given the children are even yet to be properly reunited with their families following the rescue last week.
Mr Dowds continued: "There is certainly a period of time required where they can absolutely put all of the efforts into ensuring that the children and the families are given all they need to fully recover, before we move on to contemplating other aspects..."
Pure Flix Entertainment, which also released the 2017 film adaptation of Lee Strobel's book The Case for Christ, said the movie would not necessarily be a Christian production but "an inspirational one".
Acknowledging how only limited information about Compassion's sponsor child has been available, Mr Dowd added: "We believe that he is relatively healthy - given the circumstances that he's just been through - but obviously they want to continue to undertake a series of medical tests, just to check that he is completely healthy."
One of the rescued boys
Click here to listen to Compassion UK's Justin Dowds speaking with Premier's Alex Williams:
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