The interview came after Putin signed a decree approving the new concept of Russia's foreign policy.
The document updates and revises key areas, goals, and tasks of the country's foreign policy to reflect the changes on the global stage in the past three years.
Speaking to Sputnik, Abzalov specifically underscored Russia's ever-increasing role in the international arena.
"Now the main agenda is related to cooperation, the threat of international terrorism, the work in the direction of Southeast Asia and the balance of power in the EU," according to him.
"Unlike previous years, when Moscow was in a defensive pattern of diplomatic relations, now it plays a more active role in the world. This is something that added to some changes in Russia's basic diplomatic document which has been signed," Abzalov said referring to the country's new foreign policy concept.
The need to make amendments to Russia's foreign policy concept was caused by "the current reality taking shape in the world," he pointed out.
"It is safe to say that Moscow is beginning to call the shots which is why the diplomatic approach is being changed," he added referring to a wide array of pressing international issues Russia will have to deal with.
Abzalov also noted that it is no accidental that the announcement of Russia's new foreign policy concept coincided with President Putin's State of the Nation Address to the Russian Federal Assembly.
According to him, a full-fledged presentation of the document on the day of Putin's State of the Nation Address is a very important signal.
"First and foremost, it is a signal to the world about how Moscow will act. Moscow advocates a model in which all countries have a combined responsibility and are on a level playing field. Apart from upholding its interests, Russia is seeking to lay down a single set of rules, something that Washington unsuccessfully tried to do," Abzalov concluded.
Russia's new foreign policy concept focuses on a wide range of urgent issues, including the country's relations with the US and NATO, the situation in Syria and arms reduction.
Also, Moscow calls for a political settlement in Syria, and its unity, independence and territorial integrity. As for the fight against terrorism, the focus should be placed on the creation of a full-blown international coalition, according to the document.
Additionally, the new Russian foreign policy concept cites new technologies that Moscow will use in order to strengthen the position of Russian media abroad and protect the country's information security.