Only one of six reactors at the Zaporizhzhia facility was connected to the electricity grid on Sunday, and Russia's main pipeline carrying natural gas to Germany remained shut down.
The fighting in Ukraine and related disputes over pipelines lie behind the electricity and natural gas shortfalls that have worsened as Russia's war in Ukraine, which began on February 24, grinds on for a seventh month.
Both issues will take centre stage this week.
UN nuclear agency inspectors are scheduled to brief the Security Council on Tuesday about their inspection and safeguard visit to the Zaporizhzhia power plant.
European Union energy ministers were slated to hold an emergency meeting Friday in Brussels to discuss the bloc's electricity market, which European Commission President Ursula von der Leyen has said "is no longer operating."
Much of the Zaporizhzhia region, including the key city of Melitopol, lost power on Sunday.
But it was later restored, said Vladimir Rogov, the head of the Russia-installed local administration in Enerhodar, the city where the nuclear power plant is located.
To the southwest, power was also out in several parts of the port city of Kherson, according to Russia's Tass news agency.
While Rogov said no new shelling of the area around the six-reactor Zaporizhzhia plant was reported on Sunday, the effects of earlier strikes lingered.
The International Atomic Energy Agency said on Saturday that the plant was disconnected from its last main external power line and one reactor was disconnected because of grid restrictions.
Another reactor was still operating and producing electricity for cooling and other essential safety functions at the site, as well as externally for households, factories and others through a reserve power line, the IAEA said.
Russian forces have held the Zaporizhzhia facility, Europe's largest nuclear plant, since early March, with its Ukrainian staff continuing to operate it.
IAEA Director-General Rafael Grossi said he will brief the UN Security Council on Tuesday on a mission he led to the plant last week.
The 14-member delegation braved gunfire and artillery blasts to reach the plant last Thursday after months of negotiations to enable passage through the fighting's front lines.
Without blaming either warring side, Grossi said his big concerns are the plant's physical integrity, its power supply and the staff's condition.
Europe's energy picture remained clouded by the war in Ukraine.
Just hours before Russian energy company Gazprom was due to resume natural gas deliveries to Germany through a major pipeline after a three-day stoppage, it announced Friday that it couldn't do so until oil leaks in turbines are fixed.
That the latest development in a saga in which Gazprom has advanced technical problems as the reason for reducing gas flows through Nord Stream 1 — explanations that German officials have rejected as a cover for a political power play.
Dismissing Gazprom's latest rationale for the shutdown, Germany's Siemens Energy - which manufactured turbines the pipeline uses - said turbine leaks can be fixed while gas continues to flow through the pipeline.
Von der Leyen blamed Russian President Vladimir Putin's war against Ukraine for Europe's energy crisis. Before the EU energy ministers' meeting this coming Friday, she said electricity and natural gas prices should be decoupled and that she supports a price cap on Russian pipeline gas exported to Europe.
Natural gas is one of the main fuels used in electricity generation, and is a major source of Russia's income, along with oil exports.
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