As winter approaches and Ukraine’s energy infrastructure remains vulnerable to Russia’s continued aerial bombardment, President Volodymyr Zelensky of Ukraine is saying that about 40 percent of his country’s power grid is “seriously damaged” and is pleading for the European Union to help rebuild.

Ukrainians have already had to adapt. In Kharkiv, in northern Ukraine, some residents are using plastic sheeting to cover the broken windows in their bedrooms. In Kyiv, the country’s capital, rolling blackouts have become a daily hardship.

More than 800,000 homes across Ukraine have been damaged or destroyed since the war began in February, with so many windows shattered by explosions that glass is scarce.

On Wednesday, Kyiv’s mayor, Vitali Klitschko, said the city had set up 1,000 heating stations stocked with generators where residents would be able to warm up, drink tea and charge their phones in the event missile attacks knock out heat and power to the city.

In recent weeks, as Russian troops have lost ground on the battlefield in the south and the east, Moscow is relying more on long-range weapons to destroy Ukraine’s power plants, lines, substations and other parts of the grid. The aim appears to be to cut off power and water to Ukrainians and erode their will to fight. On Monday, Kyiv was without water and electricity for most of the day after the latest round of Russian missile and drone strikes.

Against that stark backdrop, Mr. Zelensky said on Tuesday that Ukraine needed more aid from the West to restore its energy grid and support its battered economy. “The issue of energy goes hand in hand with the financial crisis and the shortage of weapons,” he said in a statement.

“Russia’s energy terrorism” has damaged “thermal power plants, combined heat and power plants and hydroelectric power plants,” according to a statement released by Mr. Zelensky’s office.

In his nightly address, Mr. Zelensky cast Russia’s attacks as “a challenge to all of Europe.”

“Moscow will present any winter difficulties in its propaganda as alleged proof of the failure of a united Europe,” he said.

Kyiv and its European allies were demonstrating signs of unity on Tuesday. In a phone call, President Emmanuel Macron of France and Mr. Zelensky agreed to hold an international conference on Dec. 13 in Paris to discuss how to help Ukraine get through the difficult winter.

Kadri Simson, the European Union’s commissioner for energy affairs, also called on the European Commission, the bloc’s executive arm, to coordinate outreach for help in restoring Ukraine’s energy infrastructure. The European Commission noted that in addition to equipment, 25.5 million euros — the equivalent of about $25 million — had been set aside to cover the country’s most urgent needs.

Ukraine’s energy problems could soon spiral into a humanitarian crisis, the World Health Organization has warned, because a lack of access to fuel or electricity “could become a matter of life or death if people are unable to heat their homes.” Mean winter temperatures in Ukraine hover around or fall below freezing during December, January and February, according to the World Bank’s climate change website.

The W.H.O. said Ukraine’s humanitarian challenges could be deepened by the advent of winter, a recent surge in Covid-19 cases and the proliferation of attacks on civilian infrastructure.