In the name of Allah, the most Beneficent, the most Merciful.
An Islamic government is that government which rules in accordance with the laws of the Shariah. The Shariah of the government must be Islam, and their laws must also be based on the Shariah. The government must also regard as utmost importance the observance of the Islamic Shariah and they must also openly profess this. The Khalifah or Ameer of the Muslims must also be such a person who as the representative of the Prophet of Allah Sallallahu Alahi Wasalam runs and governs the country in accordance to the Shariah.
For a government to be classified as an Islamic government, it must openly profess and proclaim that its madhab is Islam. It is not sufficient to be regarded as a Muslim country if the ruler is a Muslim. Until the government does not declare that it is Islamic i.e. in accordance to the laws of the Shariah, then such a government is not classified as an Islamic government.
(Aqaaidul Islam Maulana Idris Khandlwi p.189 –p.190)
Islam is for a procedure where justice and adl prevails. As long as a particular democratic government is just and equal, then there is nothing wrong in Muslims using their systems and participating in it through being leaders or by voting.
Only Allah Knows Best
Mohammed Tosir Miah
Darul Ifta Birmingham