President Volodymyr Zelensky says Russia has widened its attacks to target Ukraine's data centres and internet providers, seeking to cause maximum disruption for ordinary people.
"All this affects people's ability to stay connected, study, work," he said.
On Friday a Russian drone hit a business centre in the capital Kyiv, killing four people and damaging a data centre. A separate attack killed a 14-year-old boy. Israel's foreign ministry said he was an Israeli citizen.
Russia confirmed it had targeted a data centre site, saying it was being used by Ukrainian military intelligence.
About 100,000 households in Kyiv and the region suffered internet outages on Wednesday due to strikes.
Some firms have already begun moving data from damaged servers to facilities abroad.
In the north-western city of Lutsk, electronic information boards at public transport stops were not working on Friday, officials said. The city council said this was "due to damage caused by a Russian attack on data centres in Kyiv".
In Friday's social media post, Zelensky wrote: "The Russians are constantly expanding their escalation operation: American and other businesses, data centres, internet providers – for Russia, all ordinary life is simply a target.
"It is important that the world responds to all of this and that Russia feels the response to its terror."
Late on Friday, Zelensky said "additional decisions" had been made at his meeting with Ukraine's top defence and security officials to protect the country's data centres and other critical communications facilities to ensure their continuous operation.
Ukraine's Foreign Minister Andrii Sybiha has said that Russia was seeking to disrupt the flow of "life-saving information" by targeting data centres.
"Rapid alerts about missile and drone threats are essential - they save lives. This is critical civilian infrastructure... It is not a military target. It is essential to keeping everyday life functioning," Sybiha said.
Zelensky's top adviser on defence technologies on Thursday admitted that "there may be local disruptions" following Russian attacks an the cost of internet services could increase to cover the costs of repairs.
But Serhii Beskrestnov stressed that Ukraine's internet network was highly decentralised, so the country "will not be left without internet access".
The data centre hit by Russia on Friday was run by Datagroup. The company said its specialists were assessing the damage after the daytime attack but all services "continue to operate from backup sites".
Kyiv Mayor Vitaliy Klitschko said on Friday evening that seven people had been killed and 59 injured after Russian overnight attacks.
Russia's defence ministry later confirmed it had hit the Datagroup site, which it said was being used by the Ukrainian military's intelligence.
Footage showing the damaged Inkom business centre that housed Datagroup has since been verified by the BBC.
The Russian defence ministry also said that over the past few days its forces have targeted a number of data processing and telecommunications centres in Ukraine, including New-Telco, United DC, Kyivstar and Parkovyi.
In recent weeks, Moscow has also intensified its strikes on Ukraine's energy and railway infrastructure – seeking to cause maximum damage as winter approaches.
Ukraine's military has been hitting Russian oil refineries and logistics hubs, saying they help finance Russia's ongoing war effort.
Russian President Vladimir Putin launched a full-scale invasion of Ukraine in 2022, and Moscow currently controls about 20% of Ukrainian territory.
Speaking to reporters late on Friday, Putin said Moscow would "give careful thought" to the idea of resuming direct peace negotiations with Kyiv, citing last week's "massive" Ukrainian attack on the capital Moscow and other recent strikes.
"It's all possible," he said, but stressed that Ukraine "must feel our retaliatory strikes", and that all decisions would be taken "based on the Russian Federation's interests".
Zelensky had earlier said he was ready for trilateral talks that would also involve the US.
Kyiv and its European allies have repeatedly accused Putin of rejecting any peace negotiations, saying he was seeking to seize more Ukrainian territory.
Speaking to the media, Putin also restated his position that Moscow had "no plans" and "no reason" to attack Europe. He had made similar statements about Ukraine, before launching his full-scale invasion almost five years ago.
In a separate development on Friday, the European Union agreed to release €6.6bn for Ukraine, the bloc's top diplomat Kaja Kallas said, describing this as "good news for Ukraine and bad news for Russia".
This includes €900 million for the EU's Military Assistance Mission for Ukraine, and a €1 billion fund for joint procurement of equipment, she said on X.
"Moscow's hybrid attacks try to intimidate Europe into scaling back its support for Ukraine. Europe is doing the opposite."
Meanwhile, Poland's prosecutors opened an investigation in what they said was an arson attack on a Starlink satellite station in Wola Krobowska on Wednesday.
In a statement, the national prosecutor's office said "there is a reasonable suspicion... that the perpetrators acted on the orders of the Russian special services". Moscow has not commented.
The station transmits internet traffic through Poland to countries including Ukraine, and uses SpaceX systems that provide connectivity via Starlink terminals.
In recent weeks a number of European Nato members have warned Russia may be preparing hybrid attacks to test their commitment to supporting Ukraine, which Moscow denies.
Earlier this month, Germany blamed Russia for an attempted drone attack on Leipzig/Halle Airport, while France has ordered a plan to protect critical infrastructure and defence industry sites.
