The social services in the south-western Norwegian town of Stavanger were also continuing to evaluate whether it would be possible to place the children in the custody of their uncle, who lives in India but is currently in Norway.
"We are hoping for a quick clarification," the couple's lawyer Svein Kjetil Lode Svendsen told AFP.
"For the time being, the process is moving in a positive direction. All the feedback we've received shows things are looking good," he said, adding he expected the social services to make a final decision by the middle of March.
Friday's meeting took place in the presence of the uncle, a social services representative and a member of the foster family temporarily caring for the children.
The case has attracted a lot of attention and emotion in India and took on a diplomatic dimension last month when foreign minister SM Krishna demanded that Norway "find an amicable and urgent solution to ensure that the children are returned to the biological parents".
The parents, Norwegian residents Anurup and Sagarika Bhattacharya, lost custody of three-year-old Avigyan and one-year-old Aishwarya nine months ago after child welfare services deemed they were not receiving proper care.
On television, the parents claimed the child services objected to their feeding the children by hand and sharing the same bed — common practices in India where they are seen as part of the bonding between mother and child.
The welfare services have refused to say why the children were removed, citing confidentiality, but have said such moves are made only in situations that endanger the child or where the child's needs are not sufficiently met.
According to Noopur Tiwari, a journalist with a television channel reporting the case from Stavanger, the decision to remove the children from their parents' custody was linked to the three-year-old boy suffering from attachment disorder.