More than a dozen countries have urged their citizens to leave the country amid warnings from the West of a possible imminent Russian invasion of Ukraine.
Countries such as the US, UK and Germany told their nationals to leave Ukraine.
Moscow has amassed about 100,000 troops on the Ukrainian border, but has denied any intention to invade.
During the call, U.S. President Joe Biden again warned Russian leader Vladimir Putin that any incursion would come at a cost.
Ukrainian President Volodymyr Zelensky said warnings of an invasion could spark panic, which he called “our enemy’s best friend.”
The White House warned that an invasion could happen at any time and could begin with aerial bombardment. Russia has described such allegations as “provocative speculation”.
The U.S. embassy in the Ukrainian capital Kiev has ordered non-essential staff to leave, and consular services will be suspended from Sunday, with only a “small number of consular staff” remaining in the western city of Lviv “to deal with emergencies.”
Canada is moving its embassy staff to Lviv, near the Polish border, according to Canadian media. The British ambassador to Ukraine, Melinda Simmons, said on Twitter that she and a “core team” would remain in Kiev.
Russia itself is making changes, saying it is “optimizing the staffing” of its diplomats in Ukraine, citing “possible provocations by the Kiev regime or a third country.”
Out of an abundance of caution, the United States withdrew from the country about 150 military personnel who were training Ukrainian soldiers. Dutch media said the country’s KLM announced it would stop flights to Ukraine with immediate effect.
Mr Zelensky said he had not seen any solid evidence from the West that Ukraine was about to be invaded.
“I think there is too much information in the media about a deep all-out war,” he said.
“We understand all the risks, we understand they exist. If you or anyone else has additional 100% reliable information about the Russian Federation’s invasion of Ukraine…please share it with us.”
Many countries, including Australia, Italy, Israel, the Netherlands and Japan, have told their citizens to leave Ukraine. Some countries also evacuated diplomats and their families.
Biden told Putin that any incursion would result in “a swift and heavy cost to Russia,” according to a White House note on phone conversations between U.S. and Russian leaders.
“While the United States remains prepared to engage in diplomacy … we are equally prepared for other scenarios,” it said.
The Kremlin called the call a “hysteria” between the United States and its allies, and said Putin again told Biden they had not addressed Russia’s security concerns, but it said the two leaders would continue to talk.
French President Emmanuel Macron also spoke to Mr. Putin by phone on Saturday, telling him that “a sincere dialogue is incompatible with an escalation of the situation,” according to a note released by the French embassy.
Watch: Foreign nationals making arrangements to leave
BBC foreign affairs correspondent Paul Adams
With foreign embassies evacuating staff and many countries now calling for citizens to leave Ukraine, Kiev still doesn’t seem like a city in crisis.
The government here is telling people to remain calm and united and, in a statement this morning, refrain from destabilizing and panic-building actions. President Zelensky said the country must prepare for any eventuality.
Across Ukraine, foreign citizens are scrambling to make plans. Stuart McKenzie, who has lived in Kiev for 28 years and ran a successful business, wanted to fly his wife and two sons away. But if necessary, he’s ready to pack the family into the car and drive 300 miles to Poland. He loves Ukraine and can’t believe things have gotten to this point.
At the British embassy we found tight-lipped staff loading luggage into cars and driving away, no one seemed willing to speak.
Not far to the north, across the Belarusian border, Russian military exercises are in full swing. Photos released this morning by the Russian Ministry of Defense show multiple rocket launchers launching. Moscow still says it has no plans for an invasion. But Russians can do a lot without stepping inside Ukraine.
In Kiev on Saturday, thousands marched through the city, chanting slogans, pledging allegiance to Ukraine and resisting any Russian invasion. The march was organized by a right-wing nationalist group called Gonor and anti-Zelensky far-right activist Sergiy Sternenko.
BBC correspondent Eleanor Montague said the demonstration was small, but it was the first major display of public sentiment since tensions escalated and took place in the city’s most famous square, the Maidan.
Sasha Nizelska, who works as a nanny in Kiev, told the BBC she would do everything in her power to resist the Russian attack. People of all ages who participated in the demonstration showed the same sentiment.
Tensions are rising as Russia continues to deploy troops along Ukraine’s eastern border. Russian troops are also holding military exercises north of Belarus, as well as naval exercises in the Sea of Azov in the southeast, leading to accusations that Russia is preventing Ukraine from going to sea.
Meanwhile, Russia’s Defense Ministry said it spotted a U.S. Navy submarine in territorial waters about 7,500 kilometers (4,660 miles) east of Russia. The U.S. submarine was near the Kuril Islands and failed to surface when instructed, officials said.
The Russian Defense Ministry said the destroyer Marshal Shaposhnikov took an unspecified “appropriate” action and the U.S. submarine left the area. Moscow has subpoenaed a U.S. defense official over the incident.
However, U.S. officials later disputed their Russian counterpart’s account of the incident.
“Russia’s claim that we are operating in its territorial waters is untrue,” U.S. military spokesman Capt. Kyle Raines said in a statement to Reuters.
“I won’t comment on the exact location of our submarines, but we do fly, sail and operate safely in international waters.”