"It is essential to change the opinion held by Russians that Ukraine is an enemy... This view should be broken," Hryshchenko told journalists.
Almost one in four Russians considers Ukraine an enemy, according to the results of an exit poll carried out in May.
The appointment of Ukraine's ex-foreign minister, who served in the government of the former pro-Russian premier, Viktor Yanukovych, on Tuesday raised hopes that relations between the two former Soviet republics would improve.
Relations between Russia and Ukraine have deteriorated recently following Kiev's NATO membership bid and its demand that Russia's Black Sea Fleet withdraw from its naval base in Sevastopol (the Crimea). The two countries have also been involved in regular gas disputes.
However, the ambassador said Ukraine's current policy towards Russia would remain unchanged, but added that a "shift" is expected. "I hope that the balance in relations between our countries will change for the better," the diplomat said.
Hryshchenko, 55, also a former Ukrainian ambassador to the U.S., was appointed first deputy head of Ukraine's National Security and Defense Council in April this year and will retain the post.
The diplomat also said he hoped that the countries would hold talks on "key" bilateral issues in the near future.
