Russian Defense Minister Sergei Shoigu (pictured above, center) told US Secretary of Defense Chuck Hagel that the decision to pull back the troops came after Moscow had received assurances from Ukraine that its army would not be deployed against civilians.
"Russia was forced to launch large-scale exercises near the border with Ukraine, facing the prospect of (Ukrainian) military action against civilians," a Russian defense ministry statement quoted Shoigu as saying.
"Once the Ukrainian authorities declared that they would not use regular military units against the unarmed population, the Russian troops returned to barracks," he added.
A Pentagon statement also confirmed that Hagel had received assurances from Shoigu that Moscow had no intention of launching a military invasion of Ukraine.
At the same time though, tensions remained high, with Hagel demanding that Russia end what he termed its "destabilizing influence inside Ukraine" and warning that "continued aggression would further isolate Russia and result in more diplomatic and economic pressure."
Russia's deputy foreign minister, Sergei Ryabkov, meanwhile, told the Interfax news agency that there would be a "painful" response after Washington imposed fresh sanctions on Russian individuals and firms on Monday.
Sanctions stepped up
Both the United States and the European Union imposed a fresh round of sanctions on Russia over its policy regarding the crisis in Ukraine.
The EU added 15 individuals it accuses of fomenting the unrest to a blacklist of people facing travel bans and asset freezes, bringing the total to 48. Among those added to the list were a deputy Russian prime minister, Dmitry Nikolayevich Kozak, and a deputy chairperson of the State Duma, Ludmila Ivanovna Shvetsova, as well as Valery Vasilevich Gerasimov, the chief of staff of the country's armed forces.
The US also imposed travel bans and asset freezes on seven individuals and 17 companies with close ties to Russian President Vladimir Putin.
Tensions also remained high on the ground in eastern Ukraine, where, in the city of Slovyansk, pro-Russian separatists continued to hold around 40 people hostage, including a number of European military observers taken hostage at the weekend.
Berlin has demanded the release of the observers, four of whom are German. Speaking to reporters in Berlin on Monday, Chancellor Angela Merkel's spokesman, Steffen Seibert, said the hostages were being "held captive against every law and without any reason."
United Nations Secretary-General Ban Ki-moon also called for their release.
Meanwhile, the mayor of the Ukrainian city of Kharkiv remained in a critical condition in hospital, after having been shot in the back and undergoing emergency surgery on Monday.
pfd/hc (dpa, AP, AFP)