The Ukrainian intelligence service said the seven, including one child, were killed as women and children tried to flee the village of Peremoha near Kyiv and that "the occupiers forced the remnants of the column to turn back".
Reuters was unable immediately to verify the report and Russia offered no immediate comment.
Russia denies targeting civilians since invading Ukraine on February 24 and blames Ukraine for failed attempts to evacuate civilians from encircled cities.
Ukrainian President Volodymyr Zelenskiy said Russia 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.
It was not possible to verify his statements.
He also said about 1300 Ukrainian troops had been killed so far and urged the US and its allies to get more involved in peace negotiations.
The president suggested Russian forces would face a fight to the death if they sought to enter the capital.
"If they decide to carpet bomb (Kyiv), and simply erase the history of this region, the history of the Kyivan Rus, the history of Europe 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," he told a news conference.
Zelenskiy discussed the war with Chancellor Olaf Scholz and President Emmanuel Macron, and the German and French leaders then spoke to Putin by phone and urged the Russian leader to order an immediate ceasefire.
A Kremlin statement on the 75-minute call made no mention of a ceasefire and a French presidency official said: "We did not detect a willingness on Putin's part to end the war".
The RIA news agency quoted Kremlin spokesman Dmitry Peskov as saying crisis talks between Russia and Ukraine, which had been conducted in person in Belarus, have continued via a video link.
Peskov said Putin had briefed Macron and Scholz in the call about the negotiations held in video format in recent days.
He said Vladimir Medinsky, who headed Russia's delegation at the in-person talks, would continue to lead the negotiations on Russia's behalf.
Russian Deputy Foreign Minister Sergei Ryabkov accused the US of escalating tensions and said the situation had been complicated by convoys of foreign arms shipments to Ukraine that Russian forces considered "legitimate targets".
Russian rocket attacks destroyed a Ukrainian airbase and hit an ammunition depot near the town of Vasylkiv in the Kyiv region on Saturday, Interfax Ukraine quoted its mayor as saying.
The exhausted-looking governor of Chernihiv gave a video update in front of the ruins of the city's Ukraine Hotel, which he said had been hit.
"There is no such hotel any more," Viacheslav Chaus said, wiping tears from his eyes.
"But Ukraine itself still exists, and it will prevail."
UK defence officials said fighting northwest of the capital continued, with the bulk of Russian ground forces 25km from the centre of Kyiv, which they have said Russia could attack within days.
Kharkiv, Chernihiv, Sumy and Mariupol remained encircled under heavy Russian shelling, the UK defence ministry said.
The Russian bombardment of Ukraine has trapped thousands of people in besieged cities and sent 2.5 million Ukrainians fleeing to neighbouring countries.
Zelenskiy said the conflict meant some small Ukrainian towns no longer existed.
Ukrainian officials had planned to use humanitarian corridors from Mariupol as well as towns and villages in the regions of Kyiv, Sumy and some other areas on Saturday.
The governor of the Kyiv region, Oleksiy Kuleba, said fighting and threats of Russian air attacks were continuing on Saturday morning although some evacuations were proceeding.
The Donetsk region's governor said constant shelling was complicating bringing aid into the southern city of Mariupol.
"There are reports of looting and violent confrontations among civilians over what little basic supplies remain in the city," the UN's Office for the Coordination of Humanitarian Affairs said.
People were boiling ground water for drinking, using wood to cook food and burying dead bodies near where they lay, a staff member for MSF in Mariupol said.
Ukraine has accused Russian forces of kidnapping the mayor of the southern city of Melitopol, which Russia controls.
Zelenskiy called on Saturday for his release and more than 2000 residents protested outside the city administration building to demand the release of Ivan Fedorov, Ukrainian officials said.
Russia has not commented on the fate of Fedorov.
