It comes after a vote in the Duma.
The EU's foreign policy chief has condemned a move by Russian MPs who have urged Vladimir Putin to recognise two separatist-held areas in eastern Ukraine as independent.
It comes following a vote in the Duma on Tuesday.
Two resolutions were presented to the lower house with the aim of recognising the self-declared Donetsk People's Republic (DPR) and Luhansk People's Republic (LPR) as independent.
Both are located in the eastern Ukrainian region of Donbas where Russian-backed separatists have been fighting Ukrainian forces since 2014.
The difference between the two resolutions is that the first one appealed directly to Putin to "immediately" recognise the two areas as independent, while the second was to be sent to Russia's foreign ministry and other governmental structures "for study and feedback".
"The EU strongly condemns the Russian State Duma’s decision to submit a call to President Putin to recognise the non-government controlled areas of Donetsk and Luhansk oblasts of Ukraine as independent entities," Josep Borrell, the EU's High Representative for Foreign Affairs and Security Policy, said on Twitter.
"This recognition would be a clear violation of the Minsk agreements."
Viacheslav Volodin, the speaker of the Duma lower house, said in a statement following the vote that "the deputies decided to send an appeal to the president".
He argued such a recognition "will create grounds for guaranteeing the security and protection of the inhabitants of the republics from external threats, as well as for strengthening international peace and regional stability in accordance with the purposes and principle of the Charter of the United Nations and will initiate the process of international recognition both states."
He accused Ukrainian authorities of violating the inhabitants' "rights and freedoms" and of operating a "complete economic blockade" of the two areas.
"Deputies of the State Duma consider the recognition of the Donetsk People's Republic and the Luhansk People's Republic justified and morally justified. Over the past years, democratic bodies and states with all the attributes of legitimate power have been built in the republics on the basis of the will of the people," he claimed.
Units 'have completed their tasks'
Such recognition would effectively sound the death knell of the Minsk Protocol — a ceasefire agreement mediated by France and Germany in the so-called Normandy Format and that came into force in 2015.
It is unclear however whether Putin would follow through as he mentioned the Minsk Agreement in his call with his French counterpart, Emmanuel Macron, over the weekend.
A round of talks in the Normandy Format was also held last week.
The Duma vote comes just hours after Moscow offered a sign of de-escalation amid a deep crisis along the Ukrainian border by announcing that some troops have started to pull back to return to their garrisons after having "completed their tasks".
Russia has deployed more than 100,000 troops over the past few months along its shared border with Ukraine, stoking fears of an invasion. Moscow has denied any plans to invade but demanded guarantees NATO will not expand to any other former Soviet nations, including Ukraine, and remove troops and weapons deployed in other eastern European nations.
It argues these are a threat to its security and violates former treaties.
Ukrainian Defense Minister Dmytro Kuleba reacted to the Russian announcement by saying; "Together with our partners, we have managed to prevent any further escalation by Russia."
He expressed caution, however, arguing that "Russia makes all kinds of statements all the time, so we have a rule: we will believe in de-escalation when we see the withdrawal of troops," he added, describing the current situation as "tense but under control."
Putin is on Tuesday meeting with German Chancellor Olaf Scholz who had demanded before embarking on his two-day trip to Kyiv and Moscow that Russia "urgently" show signs of de-escalation. He also spoke with his US and French counterparts over the weekend.
'Day of national unity'
Meanwhile, Ukrainian President Volodymyr Zelenskyy declared Tuesday "a day of national unity" in a televised address on Monday evening. Washington had warned last week that new intelligence suggested it could be the day Russia invades.
"On this day, we will hoist national flags, put on blue and yellow [the colour of the national flag] ribbons and show the world our unity," he said.
He stressed his government is "monitoring the situation, calculating different scenarios, preparing decent responses to all possible aggressive actions" and praised the country's "wonderful army".
"Our guys have unique experience and modern weapons. This is an army many times stronger than eight years ago," he added.
He also urged Ukrainians who have left the country, in particular elected officials and civil servants, to return.
"The people of Ukraine have entrusted you not only to govern the state but also to protect it. It is your duty in such a situation to be with us, with the Ukrainian people," he said.