"A government that has been imposed from abroad without the consensus of Libyans... has no place amongst us," the so-called Tripoli government said in a statement.
Libya has had two rival administrations since mid-2014 when the recognised government was forced from Tripoli to the far east after a militia alliance including Islamists overran the capital.
The United Nations is pushing Libya's rival politicians to accept the unity government, created under a power-sharing deal sealed in December.
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It has not been formally endorsed by lawmakers from either side but on Saturday the government announced it was taking office on the basis of a petition signed by lawmakers.
The United States and its European allies on Sunday called on the new unity government to swiftly move to Tripoli and take up power, threatening sanctions against those who undermine the political process.
But the Tripoli authorities said any new government would have to be the result of "an inter-Libyan accord" and its members selected "inside Libya with a transparent agenda and programme and a consensual strategy".
Libya has descended into chaos since the 2011 ouster of longtime dictator Moamer Kadhafi, allowing extremist organisations including the Islamic State jihadist group to gain ground.