Ukrainian servicemen observe a memorial for killed soldiers in central Kyiv AFP

Russian strikes killed three people in the Ukrainian city of Kharkiv, authorities said Friday, after the United States had authorised Kyiv to use American weapons to hit targets inside Russia in defence of the region.

With Russia having retaken the battlefield initiative in recent months, Ukraine had doubled down on calls to permit it to use longer-range US weapons to attack Russian territory -- something Washington had resisted over fears it could drag NATO into direct conflict with Moscow.

But that calculus changed after Russian forces launched a fresh offensive in the Kharkiv region this month.

Overnight Russian strikes on a residential area in Kharkiv city killed three people and wounded at least 23 others, including two children, regional police said early Friday, warning residents could still be trapped under the rubble.

"A man and a woman were killed as a result of an enemy munition hitting a multi-storey residential building... The fourth and fifth floors of one of the building's sections were completely destroyed," police said in a statement, adding that another munition killed a guard at a civilian production facility.

Regional Governor Oleg Synegubov noted in a Telegram post that an emergency medic was among the wounded, adding: "The enemy again used a double strike tactic, while medics, rescuers and law enforcement officers were already working on the spot."

Kharkiv Mayor Igor Terekhov said there had not been "a single military person, not a single military object" present.

Ukraine's second-largest city, Kharkiv is located just across the border from Russia's Belgorod and regularly comes under attack from Russian missiles.

Russian strikes that hit a hardware superstore in the city last weekend killed 16 people.

On the other side of the border, in Russia's southern Krasnodar region, an oil depot was damaged in an aerial attack, its governor said Friday morning, noting that a major drone incursion elsewhere in the region had been repelled by air defences.

"The situation is more serious in Temryuk district -- the oil depot infrastructure there was damaged by an air strike. Three tanks with petroleum products were damaged and are on fire," Governor Veniamin Kondratyev said on Telegram, adding some workers had been wounded.

US officials said Thursday that President Joe Biden had lifted restrictions on Ukraine using weapons supplied by the United States against targets on Russian territory, but only to defend Kharkiv.

"The president recently directed his team to ensure that Ukraine is able to use US-supplied weapons for counter-fire purposes in the Kharkiv region so Ukraine can hit back against Russian forces that are attacking them or preparing to attack them," a US official said on condition of anonymity.

A second US official confirmed the change of policy, which followed weeks of behind-the-scenes discussions between the White House and top US military and State Department officials.

Biden gave the final sign-off in recent days, but the decision was kept secret for operational reasons and only became effective on Thursday.

The White House has made it clear to Kyiv that the permission for cross-border attacks was limited to targets just over the border that were being used to launch offensives.

Ahead of a NATO meeting in Prague on Thursday, alliance chief Jens Stoltenberg had said repeatedly that it was time for members to reconsider limits on strikes inside Russia.

French President Emmanuel Macron had also insisted this week that Ukraine be allowed to "neutralise" bases in Russia used to launch strikes.

German Chancellor Olaf Scholz has remained cool to the idea, though his country did promise Ukraine a new package of military aid worth 500 million euros ($540 million) on Thursday.

The Kremlin, for its part, accused the West on Thursday of "entering a new round of escalations in tensions" in recent days.

The Pentagon, meanwhile, released a new report Wednesday citing debris analysis to confirm long-standing allegations that North Korea has been supplying Russia with weapons for use in Ukraine.

The report by the Pentagon's Defense Intelligence Agency used open-source imagery to confirm that debris found in the Kharkiv region in January was from a short-range ballistic missile made in North Korea.

"North Korean missile debris was found throughout Ukraine," the report said.

South Korea has accused Pyongyang of sending thousands of containers of munitions to Russia, which would violate rafts of UN sanctions on both countries.

The powerful sister of North Korean leader Kim Jong Un this month called the allegations "absurd".

But experts say a recent weapons testing spree in North Korea may be for munitions destined for use in Ukraine.