Ukraine's president has described the bombardment of Kharkiv, which killed dozens of civilians, as a war crime.
Volodymyr Zelensky said there were eyewitness accounts of civilians being deliberately targeted during Monday's attack on Ukraine's second largest city.
Rights groups also said war crimes may have occurred during Russia's invasion.
The International Criminal Court's (ICC) is looking to launch its own investigation into the allegations.
There is "reasonable basis" to believe war crimes or crimes against humanity have been committed in Ukraine, chief prosecutor Karim Khan said late Monday.
Days after launching its invasion, Russia is attacking Ukraine on several fronts, but its advance has been slowed by Ukrainian resistance.
Air raid sirens sounded again in the capital, Kyiv, as satellite images showed a 40-mile (64km) Russian military convoy advancing from the north of the city.
The convoy includes armoured vehicles, tanks, artillery and logistical vehicles, and is less than 18 miles (30km) away from Kyiv, according to Maxar Technologies, which released the images.
Mr Khan said his investigation would look into alleged crimes arising from the fighting, as well as violations dating back to the initial Russian invasion in 2014.
The prosecutor needs the approval of ICC judges to begin work. For now, he has asked his team to start collecting evidence of abuses, such as attacks on civilians.
Neither Russia nor Ukraine are members of the ICC, but Kyiv has accepted the court's jurisdiction.
Mr Zelensky has also called for the West to consider a no-fly zone over Ukraine - something Washington so far ruled out over fears it could draw the US into a direct conflict with Russia.
Videos shared on social media showed rockets landing in Kharkiv, in what some defence analysts described as typical of a cluster munition strike on a dense urban area.
Amnesty International called for an investigation into the assault on Kharkiv as a possible war crime.
Russia has previously denied targeting residential areas.
UK Prime Minister Boris Johnson accused Russia of "barbaric Russian airstrikes against innocent civilians, including children" and pledged more military aid for Ukraine.
Established in 2002, the ICC investigates and prosecutes genocide, war crimes and crimes against humanity.
Any Russian nationals accused of committing war crimes, crimes against humanity or genocide in Ukraine, would have to be extradited by the Kremlin before standing trial in The Hague.
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