One message on a hacking forum read: "lease of servers to prepare new attacks on the websites of the public sector, the banking sector and the defence sector".
Ukrainian authorities said they had seen online warnings that hackers were preparing to launch major attacks on government agencies, banks and the defence sector have said.
Ukraine has suffered a string of cyberattacks in recent weeks which Kyiv has blamed on Russia. Moscow, which is caught up in a mounting confrontation with the West over Ukraine, has denied any involvement.
Ukraine's government-run cybersecurity agency CERT-UA said on Monday it had found warnings on a hacking forum.
One message had "referred to the lease of servers to prepare new attacks on the websites of the public sector, the banking sector and the defence sector," it said.
Ukraine said on Tuesday that Russia was likely behind an attack that downed the web portal of the defence ministry and disrupted banking and terminal services at large state-owned lenders.
The websites and banks targeted then were hit with a distributed denial-of-service attack, or DDoS. It works by hackers flooding servers that host the website which then become overloaded and consequently shut down.
Ilya Vityuk, the Head of the Ukrainian Intelligence Agency’s Cyber Security Department, said it was too early to definitively identify specific perpetrators.
However, he said during a press conference last week: "We know today that, unfortunately, the only country that is interested in such strikes on our country, especially against the background of mass panic over a possible military invasion is, unfortunately, the Russian Federation".
The online attacks and warnings of more come as Western countries accuse Russia of planning an invasion of neighbouring Ukraine.
Moscow denies planning any attack but has demanded security guarantees including a promise that Ukraine would never join NATO.
Ukraine has previously accused Russia of launching cyberattacks to sow panic and crash its financial system.