Eight Russian missiles have been fired at the Ukrainian city of Yavoriv which is less than 15 miles from Poland and EU border.
The attack was the westernmost of the war so far, while air raid sirens again woke residents in the capital Kyiv.
"The occupiers launched an air strike on the International Center for Peacekeeping and Security" in Yavoriv, the Lviv regional military administration said in a statement.
"According to preliminary data, they fired eight missiles."
The attack was carried out at a military unit at the facility, Interfax Ukraine news agency cited Anton Mironovich, spokesman for the Academy of Land Forces of the Ukrainian Armed Forces, as saying.
"According to preliminary data there are no dead, but information about the injured and wounded is being clarified," Mironovich added.
The military training facility, the biggest in the western part of the country and traditionally the site of joint drills with NATO, is located less than 15 miles from the Polish border.
Ukrainian President Volodymyr Zelensky has warned Russian forces they face a fight to the death if they try to occupy the capital Kyiv, as air raid sirens again woke residents on Sunday morning.
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"If they decide to carpet bomb and simply erase the history of this region... and destroy all of us, then they will enter Kyiv. If that's their goal, let them come in, but they will have to live on this land by themselves," Zelensky said on Saturday.
The president, who has repeatedly appeared on social media from the capital, said some small towns no longer existed in the third week of Russian attacks, the biggest assault on a European country since World War Two.
Russian shelling has trapped thousands of people in besieged cities and sent 2.5 million Ukrainians fleeing to neighbouring countries.
Ukraine accused Russian forces on Saturday of killing seven civilians in an attack on women and children trying to flee fighting near Kyiv.
France said Russian President Vladimir Putin had shown no readiness to make peace.
The Ukrainian intelligence service said the seven, including one child, were killed as they fled the village of Peremoha and that "the occupiers forced the remnants of the column to turn back."
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Moscow denies targeting civilians since invading Ukraine on February 24.
It blames Ukraine for failed attempts to evacuate civilians from encircled cities, an accusation Ukraine and its Western allies strongly reject.
Zelensky said Moscow was sending in new troops after Ukrainian forces put 31 of Russia's battalion tactical groups out of action in what he called Russia's largest army losses in decades.
"We still need to hold on. We still have to fight," Zelensky said in a video address late on Saturday, his second of the day.
Saying about 1,300 Ukrainian troops had been killed, he urged the West to get more involved in peace negotiations.
The United States said it would rush up to $200 million in additional small arms, anti-tank and anti-aircraft weapons to Ukraine, where officials have pleaded for more military aid.
The Kremlin describes its actions as a "special operation" to disarm Ukraine and unseat leaders it calls neo-Nazis.
Ukraine and Western allies call this a baseless pretext for a war of choice that has raised fears of wider conflict in Europe.
Zelensky discussed the war with German Chancellor Olaf Scholz and French President Emmanuel Macron, who urged Putin to order an immediate ceasefire.
A Kremlin statement on their 75-minute call made no mention of a ceasefire.
A French presidency official said: "We did not detect a willingness on Putin's part to end the war."
Russian Deputy Foreign Minister Sergei Ryabkov accused the United States of escalating tensions and said the situation had been complicated by convoys of Western arms shipments to Ukraine that Russian forces considered "legitimate targets".
In comments reported by the Tass news agency, Ryabkov made no specific threat.
Any attack on such convoys before they reached Ukraine would risk widening the war.
Crisis talks between Moscow and Kyiv have been continuing by video link, said Kremlin spokesperson Dmitry Peskov, according to Russia's RIA news agency.
He gave no details, but Ukrainian Foreign Minister Dmytro Kuleba said Kyiv would not surrender or accept any ultimatums.
