"The armed and bloody coup which is being implemented aims to return Syria to Lebanon and extend Iran's reach to the Mediterranean," the Lebanese government said in a statement, after holding an emergency session.
"Violence will not terrorise us, but it will increase our resolve," it said.
Mr Siniora was reportedly holed up with several ministers in his heavily guarded in central Beirut.
The Lebanese army did not intervene to stop Hezbollah fighters from seizing large swaths of western Beirut.
The UN Security Council has urged the rival parties to stop fighting amid fears of civil war breaking out.
Lebanon was plunged into civil war from 1975-90, drawing in Syria and Israel, the two regional powers.
Analysts say the key to avoiding such a conflict this time may be the neutrality of the army, and its ability to withstand the sectarian tensions.
Syrian President Bashar al-Assad, whose country long dominated Lebanon, said on Friday that the political crisis there was an "internal matter".
Having withdrawn its army from the country in 2005, Syria denies meddling in Lebanon's internal politics.
Lebanese army on the streets of Beirut
But Damascus has been accused of involvement in the assassination over the past three years of several anti-Syrians, including Rafik Hariri, a former prime minister.
Lebanon has been without a president since late 2007, amid deadlock between the ruling coalition and Hezbollah-led opposition over the make-up of the government.
Earlier, media offices owned by Saad Hariri were shut after being attacked by militants loyal to Hezbollah.
The army moved in after gunmen besieged TV station Future News and partially set fire to the offices of al-Mustaqbal newspaper. Mr Hariri's radio station was also silenced.
'Save Lebanon from hell'
A compromise was reached for the premises to be taken over and protected by the Lebanese army at the price of going off the air.
Several Sunni neighbourhoods in western Beirut, considered strongholds of Lebanon's ruling bloc, have reportedly been over-run by militants from Hezbollah and its Shia ally Amal.
A rocket-propelled grenade hit the fence of the heavily protected home of Mr Hariri in the Koreitem neighbourhood, officials said.
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