WASHINGTON - The United States will send four more high mobility artillery rocket systems (HIMARS) to Ukraine, U.S. Defense Secretary Lloyd Austin said on Wednesday, in the latest military package to bolster Kyiv as it confronts heavy pounding by Russian forces.

Russia's Defense Minister Sergei Shoigu earlier this week ordered generals to prioritize destroying Ukraine's long-range missile and artillery weapons after Western-supplied weapons were used to strike Russian supply lines.

Nearly five months since President Vladimir Putin ordered the invasion, Russian forces are grinding through the Donbas region of eastern Ukraine and occupy around a fifth of the country.

"(We) will keep finding innovative ways to sustain our long-term support for the brave men and women of the Ukrainian armed forces and we will tailor our assistance to ensure that Ukraine has the technology, the ammunition and the sheer firepower to defend itself," Austin said at the start of a virtual meeting with allies on Ukraine.

The West has supplied Ukraine with longer-range heavy artillery and multiple launch rocket systems to help Kyiv hold out despite Russian artillery supremacy in numbers and ammunition.

Ukraine says it has carried out successful strikes on 30 Russian logistics and ammunitions hubs, using several multiple launch rocket systems recently supplied by the West.

HIMARS have a longer range and are more precise than the Soviet-era artillery that Ukraine has had in its arsenal.

Austin said the new package would also include rounds for Multiple Launch Rocket Systems as well as artillery munitions.

The latest package would bring the total number of HIMARS the United States has provided to Ukraine to 16.

The United States has provided $8 billion in security assistance since the war began, including $2.2 billion in the last month.

(Reporting by Idrees Ali; Editing by Andrew Heavens and Andrew Cawthorne)