According to sources, Gerry McCann asked one of their friends to check on Kate and the children while he had a tennis lesson.
Mr McCann spoke to David Payne shortly before 6.30pm while playing on the court at the Mark Warner Ocean Club resort in Praia da Luz.
The source said: "David Payne saw
Madeleine at around 6.30pm.
"He popped in because Gerry wanted to make sure Kate was OK. Gerry was playing tennis and David said he was going past.
"I expect it was said [by Gerry] as: 'If you are heading back that way, stick your head in and see if Kate is all right'.
The exchange between Mr Payne and Mr McCann had fuelled Portuguese suspicions about Mrs McCann's frame of mind on the day Madeleine disappeared.
Detectives in Portugal suspect she killed Madeleine by accident and that Mr McCann helped her cover up the death - which is vehemently denied by the McCanns as a smear.
But Mr Payne's evidence now forms part of the Portuguese investigation.
It is part of new details of the day which can be revealed for the first time.
A source close to the McCanns has revealed further details of events as they unfolded in the hours before Madeleine went missing from her family's holiday apartment on 3 May.
The source said Mrs McCann went jogging around Praia da Luz while Madeleine and twins Sean and Amelie played in the resort's children's club.
The McCanns then took the children for tea before Mr McCann went for an hour-long tennis lesson - starting at 6pm - with the resort's coach.
During that time, Mrs McCann was alone with the children in their two-bedroom apartment bar the crucial few minutes during which Mr Payne made his visit.
Mr Payne is understood to have told police he found Mrs McCann happily coping with her three children, including Madeleine.
Mr Payne, 41, is bound by Portuguese secrecy laws and cannot speak out about the events on that night.
But today he said: "Kate is a fantastic mum. She can cope. She is a very able person."
Mr Payne, who has known the couple for at least five years, added: " I have never witnessed anything untoward in all that time."
The source said there was now a fear Portuguese police may have misinterpreted Mr McCann's request as some indication his wife was struggling with the children and needed help.
But the source said Mr Payne, a senior research fellow in cardiovascular sciences, had "never given the impression this was a woman stressed out".
The source added: "The impression I get was Kate was having a lovely time with the children."
The evidence of Mr Payne, 41, and the McCanns' dining companions that night - dubbed the "Tapas Nine" - is vital in clearing the couple of any involvement in Madeleine's disappearance.
It is understood that none of their friends has been interviewed by Portuguese police since giving official witness statements back in May.
Portuguese newspapers claim police want to interrogate them again and that a judge has given the go-ahead.