Critics have alleged that Toronto-based Centerra Gold, which is developing Kumtor, has used accounting tricks to reduce its tax liabilities. The company has denied the allegation.
Centerra says its project has generated $1.9 billion in benefits for Kyrgyzstan, including $620 million in taxes. Kumtor accounts for 12 percent of the economy.
Some observers believe that opposition politicians may be using discontent over the mine as a smokescreen for a grab at power.
"It is clear that the situation with Kumtor was just a pretext to destabilize the situation," said political analyst Mars Sariyev.
Kyrgyzstan has seen the overthrow of two governments in its short history since gaining independence amid the collapse of the Soviet Union in 1991.
President Askar Akayev was cast out of power in May 2005 after a weeks-long sit-in protest against corruption and misrule in the center of the capital.
Five years later, several dozen were shot dead by government troops when angry mobs attacked the presidential administration building in unrest that led to President Kurmanbek Bakiyev's ouster.
The constitution introduced in 2010 created a more even balance of power between parliament and the presidency aimed at avoiding the emergence of an authoritarian leadership.
But some politicians, including Tashiyev, who was still being questioned by the security services late Wednesday, have argued that Kyrgyzstan needs to revert to a more presidential model of governance.