The targeted sites, including the emergencies ministry, education ministry and cabinet, displayed a message in Ukrainian, Russian and Polish warning Ukrainians that their personal data had been compromised.
"All information about you has become public, be afraid and expect the worst," the message read.
Within hours of the breach early Friday the SBU security services said access to most hit sites had been restored and that the fallout was minimal.
"The content of sites has not been changed and according to preliminary information no personal data was leaked," the SBU security service said in a statement.
Russian military drills
Kyiv did not immediately blame any individual or entities and the EU's foreign policy chief Josep Borrell said it was too early "to point the finger at anybody. We don't have proof".
But he added: "You can imagine who did this."
In October 2020, the United States charged six Russians with carrying out cyberattacks on Ukraine's power grid, the 2017 French elections and the 2018 Winter Olympics.
The Justice Department at the time said the six were current or former members of the GRU Russian military intelligence and were also accused of staging a malware attack called "NotPetya" that infected computers of businesses worldwide causing nearly $1 billion in losses.
The latest attack came at a time of high-voltage tensions between Russia and the West over Ukraine, a close ally of the United States and Europe.
Those ties deepened after Russia in 2014 annexed the Crimean peninsula from Ukraine and threw it weight behind pro-Moscow separatists that control sections of the east of the country.
The West has accused Russia of deploying tanks, artillery and about 100,000 soldiers on Ukraine's war-torn eastern border in recent weeks, in what NATO says is preparation for an invasion.
The US ambassador to NATO, Julianne Smith told reporters in Brussels that "we all understand there is an array of scenarios that could unfold as it relates to what's happening between Russia and Ukraine".
"And one is a full scale conventional military attack, and there are other layers to it and we'll have to see what we find out today," she said.
Moscow says it has no plans to invade Ukraine.
Footage published by the Russian defence ministry Friday showed Russian tanks and infantry carrying out firing drills near the city of Rostov-on-Don in southern Russia near Ukraine.
Moscow says this is a response to what it sees as the growing presence of NATO in its sphere of influence, where it fiercely opposes the expansion of the Atlantic alliance.
Russia also says the US-led military alliance should not admit Ukraine or Georgia as new members.
This week the United States and its NATO allies held talks with Russia in an attempt to ease tensions, but all three rounds of negotiations -- in Geneva, Brussels and Vienna -- proved unsuccessful.
Deputy Foreign Minister Sergei Ryabkov said Thursday that Moscow saw no reason to hold a new round of security talks with the West following a lack of progress.
Ryabkov also said he did not rule out the possibility that Moscow could deploy forces to allies Venezuela or Cuba if diplomacy failed.