US President Joe Biden has given Ukraine permission to use American-supplied weapons to strike targets in Russia, but only near the Kharkiv region, US officials say.

One told BBC News his team had been directed to ensure Ukraine was able to use US weapons for "counter-fire purposes" to "hit back at Russian forces hitting them or preparing to hit them".

Russian forces have made gains in the Kharkiv region in recent weeks after a surprise offensive in the area, close to the border with Russia.

On Friday, Ukrainian officials said three people had been killed and 16 injured in Russian shelling of a residential building in a suburb of Kharkiv city.

The US official also told the BBC: "Our policy with respect to prohibiting the use of Army Tactical Missile System [ATACMS] or long-range strikes inside of Russia has not changed.”

When asked by CBS, the BBC's US partner, whether the new policy included attacking Russian aircraft, an official said: "We've never told them [Ukraine] they can't shoot down a Russian airplane over Russian soil that's coming to attack them.”

The White House and state department had no immediate comment.

The UK earlier signalled that it was open to an easing of restrictions on how Ukraine could use weapons supplied by the West.

Despite concerns that such a development could further escalate the conflict, several European leaders also recently called for restrictions on the use of such weapons to be relaxed.

But Washington, which provides the bulk of Ukraine's weaponry, had resisted easing these restrictions over fears of escalation.

US Secretary of State Antony Blinken hinted at the shift during a visit to Moldova on Wednesday.

"At every step along the way, we've adapted and adjusted as necessary," he said.

"And so that's exactly what we'll do going forward."

Russian forces appear to have recently taken advantage of a window of opportunity to push deeper into Ukrainian territory in Kharkiv as Kyiv waits for further Western weapons to arrive at the front.

At least 12 people were killed and dozens more were wounded last week after Russian forces hit a supermarket in the city of Kharkiv with two glide bombs.

Early on Friday, Kharkiv regional governor Oleh Syniehubov said on Telegram that Russian shelling had struck a five-storey apartment block in the Novobavarskyi District of Kharkiv, destroying part of the building and causing a fire.

At least three people were killed and 16 were injured, including a 12-year-old boy and a 12-year-old girl, both of whom were taken to hospital, he said.

The Ukrainian official accused Russian forces of targeting "exclusively civilian infrastructure" and using a "double-strike tactic", hitting the site for a second time after paramedics and rescue workers had arrived.

There was direct hit from fpv, so that wasn't a random artillery shot

🇷🇺💥 FPV-дроны группировки "Центр" опять не оставили и шанса украинским боевикам

ВСУшники и в блиндаже укрылись, и ветками замаскировали, а наш оператор все равно залетел точно в цель и "накрыл" врагов.