Irina Antonova has been facing deportation following the rejection of application for residence to live with her daughter's family. Under current immigration legislation, grandparents cannot be granted a residence permit, as they are not considered part of the immediate family.
A member of the group that has been working on her behalf told YLE's Swedish-language service on Monday that the family feels it has been under too much pressure because of the affair.
Russian authorities have offered Antonova medical care in Vyborg and a place in a care facility for the elderly.
The support group Monday presented Minister for Immigration Astrid Thors with a petition signed by 2,200 people demanding that in future the parent of any Finnish citizen be granted residence rights, if otherwise he or she would be alone in his or her home country.
The group says it will continue to back efforts by Egyptian grandmother Eveline Fadayel to remain in Finland with her family, despite a deportation order. The petition to Immigration Minister requested that Fadayel's deportation be suspended until new legislation is in force which would allow her to legally stay.