The case involved the removal of four children from the custody of their Russian mother by Finnish officials.
President Sauli Niinistö said he had held discussions with Russian President Vladimir Putin two days ago and noted that there was nothing to suggest that relations between the two countries were strained.
Niinistö said he did not feel that he was being put to the test as a new president, but added that the issue of child custody had been discussed in the past.
He said that Russian criticism of Finland might simply be a case of Russian politicians playing to the home gallery, with Finland assuming the role of the common bogeyman for the purposes of internal politicking.
The president said that Finland would not agree to any actions that means a transfer of decision-making power elsewhere.
He added that he hoped that the case would be removed from the political agenda to be dealt with by the relevant officials.