Local rights activists say hundreds of religious Shias have been arrested in recent weeks as pro-government media report on the arrests of "spies" and "traitors" working for neighboring Iran.
His outspoken criticism of Iran, and the timing coinciding with the opening of Azerbaijan's embassy in Israel led some fellow MPs to point the finger at Tehran.
The embassy's chief of security was shot dead, and two other staff were wounded. The attack comes amid Azerbaijan's increasingly strained relations with Iran and blossoming friendship with Iran's archrival Israel.
The drills included a crossing of the river that forms the Azerbaijan-Iran border, mirroring the threat that Iran’s armed forces had made weeks earlier.