Kevin Loughlin and Lynette Thornton said yesterday that Jodi, six, and Tom, four, had been out of their sight for an "absolute maximum" of five minutes on Holme beach, near Hunstanton, Norfolk, and that they were convinced they had not drowned.
The couple, from Norwood, south London, were speaking in detail for the first time since the children vanished last Sunday.
The children, who could not swim, were last seen running towards the sea in their swimming costumes. Police combed the area for three days in the search for them.
Mr Loughlin, a computer consultant, and Ms Thornton, a physiotherapist, both 37, said they could not believe the children had drowned because the water was too shallow.
"We just have to keep looking and keep hoping, hoping that something turns up," Mr Loughlin said.
"Both Lynette and I are positive about the fact that we are going to see them again, see them alive and see them well."
Speaking at a press conference at Hunstanton police station, he added: "What is keeping us going, both Lyn and I, is that we are as convinced as we can be that they have not drowned. The water is so shallow that we don't think it is feasible and they are used to water."
Mr Loughlin, who has recently recovered from cancer, said he and his partner spent around two hours scouring the beach before calling the police.
At one point he thought he had spotted the children, but when he reached the two youngsters he had seen they were not Jodi and Tom.
Chief Inspector Kevin Coyle said: "We are not looking at this stage for any stranger."
Be safe on the beach,