The United States on Friday announced a fresh tranche of military aid for Ukraine, including ammunition, missiles, mines and artillery rounds as Russia presses its assault on the Kharkiv region.

Ukraine has been battling back in Kharkiv since May 10, when thousands of Moscow's troops stormed the border, making their biggest territorial advances in 18 months.

"The United States is announcing today a significant new drawdown of weapons and equipment for Ukraine to support the brave Ukrainian people as they defend their country," said Secretary of State Antony Blinken.

"This 275 million dollar package, which is part of our efforts to help Ukraine repel Russia's assault near Kharkiv, contains urgently needed capabilities."

Last month, US lawmakers passed a long-delayed US$61 billion military aid deal for Kyiv after months of squabbling in Congress as Ukrainian forces suffered setbacks on the battlefield due to ammunition and funding shortages.

Since then, President Joe Biden has ordered five tranches of military aid to be sent to Ukraine.

"Assistance from previous packages has already made it to the front lines, and we will move this new assistance as quickly as possible," Blinken said.

Strikes on the city of Kharkiv, Ukraine's second-largest, killed at least seven people on Thursday, local authorities said.

More than 11,000 people in the wider region have been evacuated since Russia began its new offensive, according to local governor Oleg Synegubov. (AFP)