In a diplomatic note this week, Moscow warned the United States and NATO against sending the "most sensitive" weapons for Kyiv to use in the conflict with Russia, saying such shipments were "adding fuel" to the situation and could come with "unpredictable consequences," the Washington Post reported.

The warning came the same week that US President Joe Biden pledged a new $800 million military aid package for Ukraine, including helicopters, howitzers and armored personnel carriers.

"What the Russians are telling us privately is precisely what we've been telling the world publicly -- that the massive amount of assistance that we've been providing our Ukrainian partners is proving extraordinarily effective," the Post quoted a senior administration official -- who spoke on condition of anonymity about the note -- as saying.

The State Department declined to comment on reports of the formal note.

"We won't confirm any private diplomatic correspondence," a State Department spokesperson said.

"What we can confirm is that, along with allies and partners, we are providing Ukraine with billions of dollars' worth of security assistance, which our Ukrainian partners are using to extraordinary effect to defend their country against Russia's unprovoked aggression and horrific acts of violence."

According to the New York Times citing US officials, the note was sent through normal channels, and was not signed by any senior Russian officials.

The formal correspondence indicates Russia is concerned about the United States' ongoing material support for Ukraine, an anonymous US official told CNN.

CNN also reported that one source familiar with the document said the complaint could mean Moscow is getting ready to adopt a more aggressive stance against the United States and NATO as the invasion of Ukraine continues.

Biden told his Ukrainian counterpart Volodymyr Zelensky of the new weapons aid package over the phone Wednesday, as Russia refocused its efforts eastward, the new frontline of the seven-week-old war.

"As Russia prepares to intensify its attack in the Donbas region, the United States will continue to provide Ukraine with the capabilities to defend itself," Biden said.

"This new package of assistance will contain many of the highly effective weapons systems we have already provided and new capabilities tailored to the wider assault we expect Russia to launch in eastern Ukraine."

Zelensky for his part tweeted that he and Biden had discussed the "additional package of defensive and possible macro-financial aid."

The new assistance included some of the heavier equipment that Washington had previously refused to provide to Kyiv for fear of escalating the conflict with nuclear-armed Russia, and comes after previous weapons aid already supplied to the Ukrainian army.