Only essential services and government offices are operating in Crimea after key electricity pylons connected to the peninsula were knocked down in Ukraine.
Protesters, including Crimean Tatars, are preventing the repair work.
Russia has warned of retaliatory measures.
Ukraine is planning new rules for cargo traffic for the southern peninsula, which was annexed by Russia in 2014.
There has been disruption to road and rail traffic to and from Crimea since Ukrainian nationalists and Crimean Tatars began a border blockade in September.
Crimean Tatar leader Mustafa Dzhemilev said the protesters would only let engineers repair two pylons that serve areas of mainland Ukraine - not the two linked to Crimea.
Russia does not have a land border with Crimea, which gets about 70% of its electricity from Ukraine.
Most of Crimea's two million people have been hit by the power cut.
There are also water shortages.
Public transport is still running and hospitals are using generators.
But the blackout has shut down many businesses and plunged the streets into darkness.
A state of emergency was imposed on Sunday and Monday was declared a non-working day.
The blackout forced the closure of some 150 schools.
"We are outraged by the cut-off... because a lot of us have electric cookers, we can't wash properly at the moment... our fridges are defrosting," Sevastopol resident Raisa Kazhyrnova told Reuters news agency.
Ukraine's state energy company, Ukrenergo, said the damage to the pylons was caused by "shelling or the use of explosive devices".
Ukrainian PM Arseniy Yatsenyuk said the government "is temporarily banning cargo traffic on the administrative border" between Ukraine and Crimea.
He also warned Ukraine would respond in kind if Russia introduced an embargo on Ukrainian products, as Moscow has threatened to do.
Russia is angry at Ukraine's decision to implement a free trade agreement with the EU on 1 January 2016.
Russia says the deal will undermine its producers, because EU exporters are likely to use Ukraine as a back door into the Russian market.
Russia has blamed Ukrainian nationalists and Crimean Tatar activists for the pylon damage, calling it "an act of terrorism".
Crimean Tatar activists said Russia must release "political prisoners" and let their leaders return to Crimea in exchange for the repair work.
Crimean Tatar activists accuse Russia of abusing their rights.
Crimean authorities said they had managed to partially reconnect some cities using generators.
But emergency power-saving measures have been imposed across the peninsula.
Russia has started laying undersea cables to connect Crimea to its power grid.
But the first phase will only take effect next month and the switch to Russia as the main supplier will take several years to complete.
Source: BBC News