At a press availability Wednesday, Secretary of State Antony Blinken lauded what he called a "significant new security assistance package to arm Ukraine with additional capabilities and advanced weaponry," saying it was "precisely what they need to defend themselves against the ongoing Russian aggression."

While Blinken noted the U.S. was leveling up the military equipment it was supplying to Ukraine, he described it as an extension of the administration’s longstanding game plan.

"[The package] includes more advanced rocket systems so that they can strike key targets on the battlefield in Ukraine from longer distances," Blinken said. "This is a continuation of a strategy that began even before Russia's invasion. We move quickly to send Ukraine significant amounts of weapons and ammunition so that they can repel Russia's aggression, and in turn, can be in the strongest possible position at any negotiating table that may emerge."

NATO Secretary General Jens Stoltenberg, who was also at the press availability, praised the latest round of assistance, calling it "a demonstration of real U.S. leadership."

But he added, "At the same time, we must prevent the conflict from escalating."

Blinken was pressed on how the U.S. could ensure that the rocket systems would not intensify or expand the war.

"With regard to weapons systems being provided, the Ukrainians have given us assurances that they will not use these systems against targets on Russian territory. There is a strong trust bond between Ukraine and the United States, as well as with our allies and partners," he answered.

Blinken added that none of this should surprise the Kremlin.

"Throughout this aggression, indeed, even before -- President [Joe] Biden was very clear with [Russian] President [Vladimir] Putin about what the United States would do if Russia proceeded with its aggression, including continuing to provide security systems that Ukraine needs to defend itself against the Russian aggression," he said. "So we have done exactly what we said we would do."

-ABC News' Shannon Crawford

Russian shelling in eastern Ukraine's Kharkiv Oblast over the past 24 hours left four civilians dead, the regional governor said Wednesday.

A woman was killed in the village of Zolochev, while a 12-year-old boy died in the village of Ivanivka, northwest of Kharkiv city. Two more people were killed in the village of Shestakove, northeast of Kharkiv city. Seven other civilians were injured in the region, according to Kharkiv Oblast Gov. Oleg Synegubov.

"The enemy is acting insidiously, striking at civilians and civilian infrastructure," Synegubov said in a statement via Telegram. "But he will answer for all his crimes! Ukraine will win!"

Over half of Sieverodonetsk is now likely occupied by Russian forces, including Chechen fighters, the U.K. Ministry of Defense said Wednesday in an intelligence update.

The ministry said fighting intensified in the streets of the key eastern Ukrainian city on Monday and Tuesday, "with Russian forces pushing closer to the town centre." Sieverodonetsk is located in the war-torn Luhansk Oblast of eastern Ukraine's disputed Donbas region.

"Russian ground operations remain tightly focused, with the weight of fire power concentrated within a small sector of Luhansk Oblast," the ministry said.

"Beyond the Donbas, Russia continues to conduct long-range missile strikes against infrastructure across Ukraine," the ministry added. "The strategically important bridge links Ukraine with Romania and with Ukraine's ports on the Danube, which have become critical to Ukrainian exports after the blockade of Ukrainian Black Sea ports by Russia."

The U.S. will provide Ukraine with "more advanced rocket systems and munitions," President Joe Biden confirmed in a New York Times op-ed published Tuesday.

The systems "will enable them to more precisely strike key targets on the battlefield in Ukraine," he wrote.

Russian Foreign Minister Sergei Lavrov warned last week that providing more advanced rockets would be a new "unacceptable escalation" because they could hypothetically be used to strike within Russian territory.

But Biden told reporters Monday that the U.S. will not "send to Ukraine rocket systems that can strike into Russia," and he and the administration are making efforts to emphasize that these new rocket systems will be used by the Ukrainians on the battlefield in their own country.

-ABC News' Conor Finnegan

White House national security advisor Jake Sullivan hinted Thursday of more sanctions coming against Russia in the "next week or two" aimed at targeting ways Moscow is evading sanctions already imposed.

“Where our focus will be over the course of the coming days is on evasion,” Sullivan said Thursday at the Economic Club of Washington. “As Russia tries to adjust to the fact that it’s under this massive economic pressure, what steps do they take to try to evade our sanctions and how do we crack down on that? And I think we'll have some announcements in the next week or two that identify targets that are trying to facilitate that evasion both inside Russia and beyond."

When Sullivan was asked whether sanctions will automatically be lifted if a negotiated peace deal between Russia and Ukraine is worked out, he appeared cautious with his words, saying, “a lot of that depends on what the shape and scope” of the agreement is.

“A lot of it depends on what the Ukrainians, in consultation with us and the Europeans come to agree to," Sullivan said. "You know, we're not going to do a deal over the head of the Ukrainians where we give a bunch of sanctions relief to Russia. But if some measure of sanctions relief were built in to some credible diplomatic solution led by the Ukrainians, that's something that we would happily discuss."

But Sullivan said Russian oligarchs shouldn't expect to ever get back their yachts and other assets seized under sanctions that have been imposed, saying the ultimate goal is "not to give them back” once the war is over.

“The president is actively looking at how we can deal with the fact that as we seize these assets, our goal is not to give them back. Our goal is to put them to a better use than that," Sullivan said. "But I'll be careful in what I say today because there's an ongoing kind of policy process around how we end up dealing with that question. But, rest assured, that the goal is not just to sit on them for a while."

-ABC News' Justin Gomez