"As for Russia, we will not deviate from our sovereign course," the Russian leader said in televised remarks Tuesday.
He said that Russia as a permanent member of the Security Council would work towards unity, help tackle global problems and "contribute to the settlement of acute regional conflicts".
Russia's foreign minister, Sergei Lavrov, will address the General Assembly this year.
Putin, during a televised meeting with newly appointed foreign ambassadors in Moscow, cautioned that global development was being hindered by the role of the United States abroad.
"Unfortunately, the development of a multipolar world is meeting resistance from those who are trying to retain their role as hegemon and control everything in Latin America, Europe, Asia and Africa," he said in an opaque reference to the West and the United States.
"This hegemon has been doing quite well for quite a long time, but it cannot go on like this forever, it is impossible," the Russian leader said.
Recently, Putin released a 31-page position paper declaring a "Russian World" in which Moscow is entitled to cross borders to allegedly "protect" ethnic Russians and Russian-speakers. This paper is regarded as his justification for attacking Ukraine, and observers say it might be used to justify an attack upon the Baltic States.
Moscow-backed separatists in Ukraine's eastern Donbas region said on Tuesday that they will hold referenda on becoming part of Russia from September 23 to 27.
The votes will take place in the self-proclaimed Donetsk and Lugansk republics that Russian President Vladimir Putin recognized as independent shortly before sending troops to Ukraine in February, according to officials and news agencies.
In response, Ukraine on Tuesday vowed to "eliminate" Russian threats against the war-torn country, after pro-Moscow separatists said they would hold referenda to join Russia later this week.
"Ukraine will solve the Russian issue. The threat can be eliminated only by force," said the Ukraine presidency's chief of staff, Andriy Yermak.