In an interview with the German newspaper Welt am Sonntag, the diplomat stressed that the West should try to maintain a dialogue with Moscow.
"It would be good if the new US administration had a new start with Russia and sought new contacts, new negotiations," Gabriel said.
He also noted that today's global conflicts can't be resolved without Russia's participation.
"Without Russia, we can't overcome conflicts in Syria, Libya, Ukraine and elsewhere. Barack Obama's attempt to humiliate Russia was a big mistake. I still hope that Washington will correct this mistake. At the moment, however, Washington and Moscow seem to be turning away from each other," the diplomat concluded.
"Now the pendulum has swung slightly towards a cooling in our relations, but I am sure that everything will inevitably come to the right balance, and we will unite our efforts in order to combat new challenges, because only in this way we will be able to overcome them," Putin concluded.
Relations between Russia and the Western countries have deteriorated since 2014, when the West imposed sanctions against Moscow for its alleged meddling in the Ukrainian conflict.
Since then, NATO has been boosting its military buildup in Eastern Europe. Following the July 2016 summit, the Alliance announced that it would deploy four multinational battalions to Lithuania, Latvia, Estonia and Poland. Moscow has repeatedly refuted claims that it is assisting breakaway regions in Ukraine and stated that NATO's military boosting near its borders was provocative and could lead to regional and global destabilization.