Nato has pledged to give more weapons to Ukraine and help fix critical energy infrastructure badly damaged by massive Russian missile and drone strikes.
At a summit in Bucharest, the secretary general of the military alliance, Jens Stoltenberg, accused Moscow of "trying to use winter as a weapon of war".
The Russian strikes have left millions of Ukrainians without electricity and running water in freezing temperatures.
Ukraine has for months been asking Nato for more advanced air defence systems.
Under the Geneva conventions, attacks on civilians, or the infrastructure vital to their survival, could be interpreted as a war crime.
At a gathering in Berlin, justice ministers of the G7 group of wealthy nations said they would co-ordinate investigations into alleged war crimes committed in Ukraine.
"Judicial examination of the atrocities committed in Ukraine will take years, perhaps even decades. But we will be well prepared - and we will persist for as long as it takes," said German Justice Minister Marco Buschmann.
Russian President Vladimir Putin - who ordered a full-scale invasion of Ukraine on 24 February - and other senior Kremlin officials deny the allegations that Russian troops are committing war crimes.
In a separate development on Tuesday, Ukraine's First Lady Olena Zelenska told lawmakers in the UK Parliament in London that Ukrainians were going through a terror similar to that experienced by the UK in World War Two, when Nazi Germany bombed cities in the blitz.
"Victory is not the only thing we need, we need justice," Mrs Zelenska said, adding she "came to you for justice, because it will lead to the end of this war".
Speaking at the start of the two-day gathering of Nato foreign ministers in the Romanian capital, Mr Stoltenberg said: "Russia is actually failing on the battlefield. In response to that they are now attacking civilian targets, cities because they're not able to win territory."
His words were echoed by UK Foreign Secretary James Cleverly, who said that Russia was aiming to "freeze the Ukrainians into submission".
Later on Tuesday, Nato issued a statement that said Russia's persistent attacks on Ukrainian civilian and energy grids were "depriving millions of basic human services".
Nato members would assist Ukraine in repairing its energy infrastructure and protecting people from missile attacks, the statement added.
And appearing at a joint news conference with Ukrainian Foreign Minister Dmytro Kuleba, Mr Stoltenberg said: "We will stand by Ukraine as long as it takes, we will not back down.
"We realise that it is extremely important that President Putin is not able to win in Ukraine. That will be a tragedy for Ukraine, but it will also make the world more dangerous and much more vulnerable."
Meanwhile, Mr Kuleba said that last time he met senior Nato officials his three words were "weapons, weapons, weapons".
"Today I have three other words, which are faster, faster and faster. We appreciate what has been done, but the war still goes on. Decisions on weapons and production lines have to be made faster," Mr Kuleba added.
Estonian Foreign Minister Urmas Rainsalu later told BBC World Service's Newshour programme that Nato needed to give missiles to Ukraine that can hit inside Russian territory.
"The most logical way to help them is to give them the capabilities to effectively get into these places from where the missiles are launched.
"All options should be on the table... there should be no red lines or caveats… we should not make any limitations," Mr Rainsalu said.
The US-led Nato alliance has repeatedly ruled out supplying longer-range missiles and other such weaponry to Ukraine, amid concerns that this could lead to a major escalation with a nuclear-armed Russia.
In Ukraine, energy workers across the country are continuing their daunting task of repairing power and water supplies to millions of people, amid warnings that Russia maybe preparing a new wave of missile attacks.
The country's power operator Ukrenergo said on Tuesday that 30% of the country's electricity needs were still currently not being met, and power rationing would continue.
Winter is setting in in Ukraine, with snow and sub-zero temperatures in many regions.
There are fears that people across the country could die of hypothermia.