Russia's entire banking sector is at risk if the Kremlin orders a further invasion of Ukraine, a United States official said Tuesday, with two of the country's banks so far targeted by U.S. sanctions.

"No Russian financial institution is safe if this invasion proceeds," the official told reporters after the announcement of sanctions against the VEB state development bank and PSB, which is tied to the defense sector.

The official, who asked not to be identified, said that further attacks on Ukraine could see sanctions against big state banks Sberbank and VTB.

Export controls stopping the flow of high-tech components to Russia are also a "key component of our potential sanctions," the official added, calling the measures "really potent because we're talking about critical technology that Russia needs to diversify its economy."

U.S. President Joe Biden on Tuesday announced tough new sanctions on Russia for "beginning" an invasion of Ukraine but said there was still time to avoid war, even as Vladimir Putin signaled plans to send troops beyond Russia's borders.

Biden also said he was hopeful diplomacy is still available, adding that the U.S. had no intention of fighting Russia.

The "full blocking sanctions" on VEB and PSB, as well as their subsidiaries, means the financial institutions will have any foreign assets frozen and will be prohibited from using the U.S. banking system.

The U.S. Treasury Department said Tuesday that it has imposed additional sanctions on five Kremlin-connected Russian individuals on top of sanctions announced by Biden.

They include Aleksandr Bortnikov, the director of the Federal Security Service and a permanent member of the Security Council of the Russian Federation, and his son.

Others include Sergei Kiriyenko, the first deputy chief of staff of the presidential office, and his son, and Petr Fradkov, the chairperson and CEO of Promsvyazbank Public Joint Stock Company (PSB).

Treasury Secretary Janet Yellen said in statement, "We continue to monitor Russia's actions and if it further invades Ukraine, the United States will swiftly impose expansive economic sanctions that will have a severe and lasting impact on Russia's economy."

However, the initial U.S. penalties cover fewer financial institutions than the European Union's, omitting the country's largest and most important bank, and did not sever the country from the SWIFT system used to move money around the globe.

Nor did Biden resort to export controls, which would have cut Russian firms off from key high-tech equipment and software, which some analysts said was a possibility.

"Today's action constrains Russia's ability to finance defense-related contracts and raise new funds to finance its campaign against Ukraine," the Treasury statement further said.

"VEB and PSB are state-owned institutions that play specific roles to prop up Russia's defense capability and its economy," it added.

While VEB has a $53 billion asset portfolio servicing Russia's sovereign debt with a loan portfolio of over $20 billion, PSB services nearly 70% of Russia's defense contracts and provides banking and personal finance to Russian military personnel, it noted.

In addition, the sanctions included five vessels owned by PSB – two container ships, two oil tankers and one cargo vessel.