In a speech Tuesday at the White House, Biden said to Russian citizens that the US and its allies are not a threat to them.
"The United States and NATO are not a threat to Russia. Ukraine is not a threat to Russia. Neither the US nor NATO have missiles in Ukraine. We do not -- do not -- have plans to put them there, as well. We're not targeting the people of Russia; we do not seek to destabilize Russia. To the citizens of Russia, you are not our enemy," Biden said.
WATCH: President Biden's full remarks
The President sounded optimistic that diplomacy would resolve the crisis after Russia publicly proposed to continue talks.
"We should give the diplomacy every chance to succeed and I believe there are real ways to address our respective security concerns," Biden said.
Russia has amassed more than 130,000 troops near Ukraine's border in recent weeks, according to US estimates, raising fears from Western and Ukrainian intelligence officials that an invasion could be imminent. Russia announced earlier Tuesday that some of its troops would return to base after completing recent drills, but stressed that major military exercises would continue.
The Russian defense ministry said troops from its Southern and Western military districts -- parts of which are next door to Ukraine -- had begun to return to their home stations, though the announcement did not say precisely where those troops were permanently based, where they had been exercising, or how many of them were withdrawing.
US Ambassador to NATO Julianne Smith said Tuesday the US was "monitoring the situation" after the Kremlin's troop announcement, but added that the US "will have to verify" any claims of a potential move towards de-escalation by Russia.
Biden held phone calls with Russian President Vladimir Putin and Ukrainian President Volodymyr Zelensky over the weekend.
A senior Biden administration official called the Putin call "professional and substantive," but said, "There was no fundamental change in the dynamic that has been unfolding now for several weeks." And a White House statement on Sunday's Ukraine call indicated that Biden said the US would respond "swiftly and decisively" if Russia takes further steps toward invasion.
Last week and through the weekend, Biden's national security adviser, Jake Sullivan, publicly warned that a Russian invasion of Ukraine could happen in the coming days.
"We cannot perfectly predict the day, but we have now been saying for some time that we are in the window, and an invasion could begin, a major military action could begin by Russia in Ukraine any day now -- that includes this coming week, before the end of the Olympics," Sullivan told CNN's Jake Tapper on Sunday's "State of the Union."
He added, "The way they have built up their forces, the way they have maneuvered things in place, makes it a distinct possibility there will be major military action very soon. And we are prepared to continue to work on diplomacy, but we are also prepared to respond in a united and decisive way with our allies and partners should Russia proceed."
The US and other nations have warned their citizens in recent days to leave Ukraine. And on Monday, US announced it would be temporarily relocating its embassy in Kyiv to Lviv, a city in western Ukraine "due to the dramatic acceleration in the buildup of Russian forces," Secretary of State Antony Blinken said.
The Russian Ministry of Foreign Affairs on Friday accused Western countries and the press of spreading a "large-scale disinformation campaign" about an allegedly impending Russian invasion of Ukraine "in order to divert attention from their own aggressive actions."
"At the end of 2021 and the beginning of 2022, the global information space faced a media campaign unprecedented in its scale and sophistication, the purpose of which is to convince the world community that the Russian Federation is preparing an invasion of the territory of Ukraine," the Ministry said in a statement published on its website.
CNN's Stephen Collinson writes the Ukraine crisis is largely a creation of Putin and his personal and disputed version of history, which that holds that the country, which was part of the Soviet Union until its breakup in 1991, should be part of greater Russia. There is also a deep resentment about how the Cold War ended with the admission of former Warsaw Pact nations, which were aligned with the Soviets -- like Poland, Romania and the Baltic states -- into NATO.
While the alliance is defensive in nature, Putin sees its move into eastern Europe as a direct threat to Russia and his notion that Moscow is entitled to a sphere of influence in the region. Ukraine is not a NATO member so the US will not send troops to defend it. But Washington also says it should not be up to Putin to decide the destiny of another independent, sovereign democracy.
In effect, Putin is holding Ukraine hostage with a demand for the withdrawal of NATO forces from eastern Europe that would amount to a major rewriting of the post-Cold War world that Washington will never accept. But he may perceive a historic moment in which he can open divisions in the alliance, forever crush Ukrainian dreams of joining the West, avenge the fall of the Soviet Union and advance his notion of Russian greatness.
As tensions have escalated, Western allies have offered increasing forms of aid and assistance, including lethal aid. The US has shipped weapons supplies and ammunition to Ukraine and offered a sovereign loan guarantee to Ukraine of up to $1 billion to support its economic reform agenda and continued engagement with the International Monetary Fund.