With Russia's invasion in its third week, the Ukrainian intelligence service said the seven, including one child, were killed on Saturday as they fled the village of Peremoha 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. 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.
Ukrainian President Volodymyr Zelenskiy said earlier that 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. It was not possible to verify his statements.
He also said about 1300 Ukrainian troops had been killed so far and urged the West 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 ... 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 said.
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 him 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".
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, but any attack on such convoys before they reached Ukraine would risk widening the war.
Responding to Zelenskiy's call for the West to be more involved in peace negotiations, a US State Department spokesman said: "If there are diplomatic steps that we can take that the Ukrainian government believes would be helpful, we're prepared to take them."
Crisis talks between Moscow and Kyiv have been continuing via a video link, Kremlin spokesperson Dmitry Peskov was quoted as saying by Russia's RIA news agency. He gave no details but Ukrainian Foreign Minister Dmytro Kuleba said Kyiv would not surrender or accept any ultimatums.
Zelenskiy later on Saturday said he had spoken to Israeli Prime Minister Naftali Bennett about the prospects for peace talks. Bennett met with Putin and previously talked by phone to Zelenskiy, but the diplomatic efforts so far have appeared fruitless.
Air raid sirens blared across most Ukrainian cities on Saturday, local media reported.
Russian rocket attacks destroyed a Ukrainian airbase and hit an ammunition depot near the town of Vasylkiv in the Kyiv region, Interfax Ukraine quoted its mayor as saying.
Britain's defence ministry said fighting northwest of the capital continued, with the bulk of Russian ground forces 25 km from the centre of Kyiv, which it has said Russia could attack within days.
The Russian bombardment 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.
The United States said it would rush up to $US200 million ($A274 million) in additional small arms, anti-tank and anti-aircraft weapons to Ukraine, where officials have pleaded for more military aid.
Russia calls its actions in Ukraine a "special operation" that it says is not designed to occupy territory but to destroy its neighbour's military capabilities and "de-Nazify" the country.
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.
But Russian shelling threatened attempts to evacuate trapped civilians, they said.
Still, around 13,000 people were evacuated from Ukrainian cities on Saturday, said Deputy Prime Minister Iryna Vereshchuk. It was almost twice the number who got out the previous day but far fewer than on the two days prior to that.