US President Joe Biden warned he would move with allies to respond to the cyber hacks and said a Russian attack remained a possibility.
East-West relations are facing one of their deepest crises in decades over Ukraine, post-Cold War influence on the continent, and energy supplies.
Europe and the United States want Moscow to reverse the build-up of more than 150,000 soldiers near the Ukrainian border, according to US estimates. They have suggested arms control and confidence-building steps to defuse the standoff.
On Tuesday, Russia published footage to demonstrate it was returning some troops to base after exercises. Biden said the United States had not verified the move. "Our analysts indicate that they remain very much in a threatening position," he said.
Ukraine did not say who it believed was responsible for the cyber attack, but a statement suggested it was pointing the finger at Russia.
"It is not ruled out that the aggressor used tactics of dirty little tricks because its aggressive plans are not working out on a large scale," said the Ukrainian Centre for Strategic Communications and Information Security, which is part of the culture ministry.
Ukrainian bank Privatbank users reported problems with payments and a banking app, while Oshadbank said its systems had slowed down.
Russia's Federal Security Service did not immediately reply to a request for comment from Reuters.
"If Russia attacks the United States or our allies through asymmetric means like disruptive cyber attacks against our companies or critical infrastructure, we're prepared to respond," Biden said in televised remarks from the White House.
One European diplomat said the hacking was concerning because a full military attack on Ukraine would likely be preceded by a cyber attack.
"It could mean a physical attack is imminent, or it could mean Russia is continuing to mess with Ukraine," the diplomat said, on condition of anonymity.
The cyber attack was marked by distributed denial-of-service attacks, when hackers flood a network with unusually high volumes of data traffic to paralyse it. Such incidents are difficult to attribute but the European diplomat said there was no doubt that Russia was behind it.
Diplomatic efforts continued on Tuesday.
Secretary of State Antony Blinken told Russian counterpart Sergei Lavrov during a call that there needed to be "verifiable, credible, meaningful de-escalation" by Moscow.
NATO's chief welcomed signals from Russia in the past two days that it may be looking for a diplomatic solution but urged Moscow to demonstrate its will to act.
"There are signs from Moscow that diplomacy should continue," NATO Secretary-General Jens Stoltenberg told reporters.
He said Russia often left military equipment behind after exercises, creating the potential for forces to regroup.
At a joint news conference with German Chancellor Olaf Scholz, Russian President Vladimir Putin referred only briefly to the troop moves and did not go into details.
Russia has always denied planning to invade Ukraine, saying it can exercise troops on its own territory as it sees fit. It has been pressing for a set of security guarantees from the West and wants to stop Kyiv ever joining NATO.
Putin told reporters Russia would not be satisfied with talk that Ukraine was not ready to join the western military alliance any time soon and was demanding that the issue be resolved now.
"As for war in Europe... about whether we want it or not? Of course not. That is why we put forward proposals for a negotiation process, the result of which should be an agreement on ensuring equal security for everyone, including our country," he said.
Russia's show of force near Ukraine's borders has prompted months of frantic Western diplomacy and drawn threats of severe sanctions if it invades, culminating in a crescendo of warnings in recent days that this could happen at any time.
The Kremlin sought to portray its moves as proof that Western talk of war had been both false and hysterical.
"February 15, 2022 will go down in history as the day Western war propaganda failed. Humiliated and destroyed without a single shot fired," Foreign Ministry spokeswoman Maria Zakharova said.
Russia's defense ministry published footage showing tanks and other armored vehicles being loaded onto railway flatcars. Western military analysts said they needed more information to judge the significance of the latest troop movements.
Commercial satellite images taken on Sunday and Monday showed a flurry of Russian military activity at several locations near Ukraine.
Russian shares, government bonds and the rouble rose sharply on hopes the situation was easing, and Ukrainian government bonds rallied.