"We will also hold this stance during discussions of this issue next week at the UN General Assembly," Lukashevich said.
Ban said that he intended to run for a second term at a news conference in New York in early June.
France and China have already stated that they would support Ban's candidacy, whose term of office expires on December 31 this year.
UN secretary generals are elected upon the recommendation of the UN Security Council represented by 192 countries. In reality, however, a candidate for this post is elected by five veto-wielding UN Security Council permanent members, which are Britain, China, Russia, France and the United States.