"We are committed and determined that we will bring back the children home at any cost," CPI(M) MP Brinda Karat, who accompanied the grandparents of the children to the meeting, quoted Krishna as saying.
Talking to reporters, the kids' grandfather Manatosh Chakraborty said they were satisfied with their meeting and hoped some "positive" results will emerge.
This is the first time that the government has sent a special envoy abroad in connection with such type of cases and "we feel optimistic", he added.
During the interaction, the Minister informed that talks held between the special envoy Secretary (West) Madhusudhan Ganapathi and Norwegian authorities has been "constructive", Karat said.
When asked about problems that could arise in event of extension of visa, Karat said they should wait till the envoy returns back to get the details on all this and other related issues.
She said the parents have appealed to the higher court there against the judgement of the lower court which has ruled the children are to be in Norway till they are 18.
"So in appeal against that, we want to make sure the child protection services there come to an agreement," she said.
Norwegian child welfare officials have accused NRI couple Sagarika and Anurup Bhattacharya of negligence and placed their children, one-year-old Aishwarya and three-year-old Abhigyan in foster care in May last year.