Washington warned on Tuesday that Russia could attack Ukrainian government facilities in the coming days as Moscow said it would show "no mercy" over an assassination it has blamed on Ukraine.
World leaders also reasserted their support for the country on the eve of its independence day celebrations and the six-month anniversary of the beginning of Russia's invasion on February 24.
Leaders including British Prime Minister Boris Johnson and German Chancellor Olaf Scholz warned Russia against further attempts to annex Ukrainian territory in the same way it did with Crimea.
"It has never been more important for us all to stand together," Johnson said in a video address to the Crimea Platform conference in Kyiv.
Polish President Andrzej Duda attended in person, warning against any "appeasement" of Russia.
"There is no return to business as usual in relations with Russia," he said.
PAY ATTENTION: Share your outstanding story with our editors! Please reach us through firstname.lastname@example.org!
In his address, French President Emmanuel Macron vowed that the EU's support for Ukraine would continue "for the long term".
"There can be no weakness, no spirit of compromise, because it's a matter of our freedom, for everyone, and of peace everywhere around the world," he said.
Ukraine's Western allies have supplied Kyiv with billions of dollars of military equipment and imposed ever more stringent sanctions on Russia.
Moscow has accused Western powers of escalating the war with its support for Ukraine.
US security warning
As tensions grew in the capital, the US embassy in Kyiv issued a security alert and reiterated its appeal for US nationals to leave Ukraine.
"The Department of State has information that Russia is stepping up efforts to launch strikes against Ukraine's civilian infrastructure and government facilities in the coming days," it said.
Ukrainian President Volodymyr Zelensky and other officials also warned that Russia could step up attacks around the Independence Day holiday.
The celebrations will be muted this year and large gatherings have been banned in the capital Kyiv.
There is also mounting concern after Russia accused Ukrainian intelligence of being behind the assassination of the daughter of a prominent ultranationalist intellectual in Moscow on Saturday.
"The investigation will hopefully be completed soon," Russian Foreign Minister Sergei Lavrov said at a press conference in Moscow.
"According to the results of this investigation, there can be no mercy for those who organised, ordered and carried out (the car bombing)," he said.
Ukraine has denied any involvement.
'War can't stop us'
Despite mounting concern, Ukraine's new football season got under way with a first match between Shakhtar Donetsk and Metalist 1925 from Kharkiv.
In the emotional pre-match ceremony, the players of both teams and the referees entered the pitch wrapped in Ukrainian flags and unfurled a banner that read "We are of the same courage."
The Shakhtar players wore T-shirts with the inscription "Donetsk. Ukraine will win" over their playing jerseys, while the players of the Kharkiv club wore similar T-shirts with the inscription "Kharkiv. Ukraine will win."
Metalist 1925 played the match wearing shirts with the emblem of Ukraine's Armed Forces instead of the traditional sponsor logo.
After a minute of silence in memory of the Ukrainians killed in the Russian invasion, the first symbolic strike on the ball was made by a Ukrainian soldier.
Matches will be held without spectators for security reasons.
But passers-by outside the stadium in Kyiv voiced their support.
Maksym Scherbyna, a fan of Dynamo Kyiv, said the resumption of football was "very important".
"We show that war can't stop us," the 35-year-old said.
Fellow fan Denys Lazarenko, 41, said: "Our country needs football very much. It unites people."