As the crisis in the region continues, Ukraine's deputy prime minister has urged Cryptocurrency and other major cryptocurrency exchanges to lock down Russian customer accounts.

"I ask all major cryptocurrency exchanges to block Russian user addresses," Mykhailo Fedorov said on Sunday.

In a tweet, Fedorov said, "It is crucial to freeze not only addresses associated with Russian and Belarusian politicians, but also those of ordinary users."

The Ukrainian minister had previously requested information on digital currency packages linked to Russian and Belarusian politicians, saying that the Ukrainian cryptocurrency community was prepared to offer a "generous reward" to anyone who provided information.

Ukraine has used Twitter to receive millions of dollars in cryptocurrency donations and has posted on online hacker forums that it is seeking help to protect itself from cyber attacks.

I ask all major cryptocurrency exchanges to block the addresses of Russian users.

It is crucial to freeze not only addresses associated with Russian and Belarusian politicians, but also those of ordinary users.

Cryptocurrency refuses to block user accounts

At the request of the Ukrainian minister, Cryptocurrency said it would not "unilaterally freeze the accounts of millions of innocent users" because that would "deviate from the reason for the existence of cryptocurrencies.

However, Cryptocurrency said, "We will take the necessary steps to ensure that those who are sanctioned have their accounts blocked."

"We are not freezing millions of innocent user accounts," a spokesperson for Coinan, the world's largest cryptocurrency exchange, told CNBC.

"Cryptocurrencies are designed to provide greater financial freedom for people around the world. A unilateral decision to ban people from accessing their cryptocurrencies would go against the very reason cryptocurrencies exist." He added.

Russia under sanctions

On Saturday, several Western countries moved to isolate Russia from the global financial system by removing the country's largest bank from the SWIFT banking system.

They also imposed restrictive measures – freezing its assets – on the Russian central bank's $630 billion in international reserves.

As the ruble fell nearly 30 percent against the dollar, Russians then withdrew foreign currency from bank ATMs in droves.

With limited access to these coins, cryptocurrency trading became the solution for people.

Kraken

Kraken, one of the largest U.S. cryptocurrency exchanges, also responded negatively to Ukraine's request, saying it was unable to freeze user accounts.

"I understand the logic of the Ukrainian order, but as much as I respect the Ukrainian people, Kraken cannot freeze our Russian customers' accounts without a legal requirement," said Jesse Powell, CEO of Kraken.

Kraken's CEO also warned that Russians need to know that such action will happen sooner or later if the authorities demand it.

"Russians should be aware that such a need may be imminent."

In a speech on Twitter, Kraken's CEO said that his own government (the U.S.) may make demands on the Russians – as seen after Canadian authorities asked to block the truckers' accounts.

The cryptocurrency exchange founder said, "If we're going to voluntarily freeze the accounts of residents of countries that unfairly attack and provoke violence around the world, then the first step is to freeze all U.S. accounts."