In the USSR the Premier was the head of government. So the Premier would handle international agreements. The President of the United States is 1) Head of State 2)Head of Government 3) Head of his political party. So neither of the two was equivalent of the President. In fact I do not believe any other democratic country has one individual in those three roles.
Sorry, one more question about this:Why did Kosygin sign the ASTP agreement and yet it was BREZHNEV who signed the ABM treaty just two days later?Thanks again for your clarification.