Most of its gas-powered heating stations have switched to alternative energy but some can only operate on gas and have had to shut down completely, our correspondent adds.
It has also received emergency gas from Hungary and Germany.
In neighbouring Bosnia, some 72,000 homes were without heating in temperatures as low as -15C. Leaders warned its gas reserves would last only a few more days.
Angry Bulgarians protested in front of the Ukrainian embassy in Sofia on Thursday, holding placards accusing Russia and Ukraine of being "gas terrorists", the Associated Press reports.
Other countries reporting a total halt in gas supplies included Romania, the Czech Republic, Slovakia, Croatia, Greece, Hungary, Macedonia and Austria.
The Czech EU presidency said late Thursday, following talks with Russian and Ukrainian officials in Brussels, that agreement had been reached with Russia over the monitors.
"This deployment should lead to the Russian supplies of gas to EU member states being restored," it said in a statement, without specifying when monitors would be in place or when gas supplies would resume.
The EU depends on Russia for about a quarter of its total gas supplies, some 80% of which are pumped via Ukraine.
Russia cut gas to Ukraine itself a week ago as the row over pricing and allegedly unpaid bills escalated.
Ukraine denies Russian accusations that it is stealing gas passing through export pipelines on its territory.
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