President Joe Biden gave Ukraine the OK to use American-made weapons to strike targets inside Russia but cautioned that the arms should be used for "counterfire purposes" to defend its second-largest city of Kharkiv from Russian attacks, according to reports.

"The president recently directed his team to ensure that Ukraine is able to use U.S. weapons for counterfire purposes in Kharkiv so Ukraine can hit back at Russian forces hitting them or preparing to hit them," a U.S. official told Politico, noting that the administration's stand on allowing long-range strikes inside Russia "has not changed."

Ukrainian officials, including President Volodomyr Zelenskyy, have been clamoring for the United States to allow them to defend Kharkiv, which is 12 miles from the Russian border, from attacks launched inside Russia.

The change will allow Kyiv to deploy U.S. weapons - rockets and rocket launchers - against Russian missiles heading toward Kharkiv, at troops gathering just over the border or Russian bombers firing bombs toward the city, Politico said.

But Ukraine cannot use the weapons to target civilian infrastructure or use long-range weapons to attack deep inside Russia.

Russian forces have been pressing military operations in the area around Kharkiv by boosting the presence of troops and attacks by cruise and ballistic missiles and drones, exploiting a delay by the United States to replenish military aid, the Associated Press reported.

The shift in policy began about two weeks ago during intensive discussions among members of the Biden administration, the report said.

Defense Secretary Lloyd Austin, national security adviser Jake Sullivan, and Gen. CQ Brown, the chairman of the Joint Chiefs of Staff, talked to their Ukrainian counterparts on May 13 who pleaded for permission to use the U.S. weapons to hit Russian positions across the border, the AP reported.

After their meeting, the three recommended Biden change his stance.

Secretary of State Antony Blinken also pressed Biden to change the policy after Zelenskyy during a visit two weeks ago made the case for using the weapons to strike Russia across the border.

Blinken hinted at the impending change Wednesday when he said the administration remained firm against Ukraine attacking deep inside Russia over fears of escalating the conflict but noted the U.S. will "adapt and adjust."

"As the conditions have changed, as the battlefield has changed, as what Russia does has changed in terms of how it's pursuing its aggression, escalation, we've adapted and adjusted, too, and I'm confident we'll continue to do that," Blinken said at a news conference in Moldova, the AP reported.