"legitimate regime" is correct and can be used in written English.
You can use it when discussing a government or system that has been accepted by the people it governs as being valid and lawful. For example: "Members of the opposition party have called for the removal of the current legitimate regime and the installation of a democratically elected government."
Russia is invited in by the legitimate regime – well, it's illegitimate in my mind – but by the regime".
Care must be taken here not to assume that the modern democratic regime, of a self-governing people, is the only legitimate regime.
Apparent translation: The vicious and unlawful destruction of Saddam Hussein's legitimate regime has shamefully thinned the ranks of the world's freedom-loving nations.
It served to legitimate regimes that constantly argued that, despite appearances to the contrary, resources were scarce and there wasn't enough money to go around; the most persuasive way of explaining why someone (else) was inevitably going to suffer.
No government in the world, or international body, would take the coup regime's side; there is no government in the world that recognizes the coup regime as the legitimate government of Honduras.
After the Vietnamese Army overthrew the Khmer Rouge, in January , 1979 the United Nations continued to recognize the deposed regime as the legitimate government of Cambodia.
As long as Egypt remains on its current path, the Obama administration should suspend all aid, keep the embassy in Cairo closed, and refrain from treating the military regime as a legitimate government".
No government in the world, including the United States, recognizes the coup regime as the legitimate government of Honduras.
As the revolution started to falter in the 1990s, he says, the nuclear option offered a way to rally nationalist opinion and "legitimate the regime".So it has proved.
The letter concluded by noting that "the invitation to the Commodore brings shame on the ITU by giving a public and global platform which he is now using to legitimate his regime".
Another rump parliament elected Sun president of a new southern regime, which claimed to be the legitimate government of China.
