It was not clear how many units were being withdrawn, and by what distance, after a build-up of an estimated 130,000 Russian troops to the north, east and south of Ukraine.
The news drew a cautious response from Ukraine and Britain but prompted a sharp rally on financial markets.
"We've always said the troops will return to their bases after the exercises are over. This is the case this time as well," Kremlin spokesperson Dmitry Peskov said on Tuesday.
He accused the United States of fueling the crisis by warning repeatedly of an impending invasion, to the point where Peskov said President Vladimir Putin had made jokes about it.
"He asks (us) to find out if the exact time, to the hour, of the start of the war has been published. It's impossible to be understanding of this manic information madness," Peskov told reporters.
Britain, which with the United States has led the warnings of imminent action, reacted cautiously.
"The Russians have claimed that they have no plans for an invasion, but we will need to see a full scale removal of troops to show that is true," Foreign Secretary Liz Truss told LBC radio.
Ukraine's Foreign Minister Dmytro Kuleba said Kyiv would only believe that Russia was moving to de-escalate the situation if it saw for itself that Russian troops were being pulled back.
"If we see a withdrawal, we will believe in a de-escalation," Interfax Ukraine quoted him as saying.
A Russian defence ministry spokesman said that while large-scale drills across the country continued, some units of the Southern and Western military districts adjacent to Ukraine had completed their exercises and started returning to base.
The Southern military district said its forces had started withdrawing from Crimea and returning to their bases after completing drills on the peninsula, which Russia seized from Ukraine in 2014.
Video footage published by the defence ministry showed some tanks and other armoured vehicles being loaded onto railway flatcars.
Russian shares, government bonds and the rouble, which have been hit by fears of impending conflict, rose sharply, and Ukrainian government bonds also rallied.
"February 15, 2022 will go down in history as the day Western war propaganda failed. Humiliated and destroyed without a single shot fired," Russian Foreign Ministry spokeswoman Maria Zakharova said.
The latest movements came after commercial satellite images taken on Sunday and Monday showed a flurry of Russian military activity at several locations near Ukraine, according to the private US company that released the pictures.
US-based Maxar Technologies pointed to the arrival of several large deployments of troops and attack helicopters as well as new deployments of ground attack aircraft and fighter-bomber jets to forward locations.
A joint exercise between Russia and Belarus is due to end on Sunday.
German Chancellor Olaf Scholz flew into Moscow on Tuesday to meet Putin in the Kremlin on the latest Western diplomatic mission to seek de-escalation.
Scholz has said he will hammer home the message from Western govenrments that they are open to dialogue about Russia's security concerns but will impose sanctions if it attacks Ukraine.
German sanctions could hit Moscow hard, but its position as Russia's number one trade partner in Europe and biggest consumer of Russian natural gas may also limit Berlin's room for manoeuvre.
Russia says it needs the West to take its security worries about NATO seriously.
The United States has warned Moscow may stage a "false flag" operation to trigger a war. Moscow has accused the West of hysteria.
