WASHINGTON — The Internal Revenue Service is pressing Congress to devote more resources to the agency as it takes an increasingly central role in the Biden administration’s efforts to prevent Russia and its oligarchs from evading the punishing sanctions that the United States has imposed.

Aides to Charles P. Rettig, the I.R.S. commissioner, told congressional staff on Wednesday afternoon that the agency’s criminal investigations unit, which has 3,000 employees, needs to grow about 40 percent over the next five years. It wants a net gain of about 1,300 after attrition. That could require Congress to invest more than $5 billion in the agency, which is trying to oversee a sprawling sanctions program and coping with evasion tactics that have become more sophisticated as a result of the proliferation of digital assets.

The Biden administration is already looking to bolster the overall I.R.S., including trying to increase its budget by $80 billion over 10 years in an attempt to crack down on tax cheats. That effort has faced resistance from Republicans, who have historically tried to starve the agency of money. The Treasury Department, which oversees the I.R.S., has not previously specified the need for funds for the criminal investigations division.

In a report circulated among members of Congress that was reviewed by The New York Times, the I.R.S. said it needed additional resources because the criminal investigations team had been asked to assist with interagency efforts to enforce sanctions related to Russia’s invasion of Ukraine. The agency asserted that investing in the division would pay off, noting that its current $600 million annual budget allowed it to identify $10.4 billion in tax fraud and financial crimes last year.

“Working with law enforcement entities across government, the I.R.S. is already in the process of investigating Russian oligarchs and those who facilitate the illegal movement of money or assets on their behalf,” the report said.

The I.R.S. has been involved in more than 20 investigations related to money laundering by oligarchs since 2017, working with other law enforcement agencies to track assets and seize property, the report said.

The criminal investigations division of the I.R.S. has a storied history; its agents have helped take down notorious tax cheats such as Pete Rose and Al Capone. Like the rest of the I.R.S., the unit has seen its budget depleted in recent years. The size of its staff declined 25 percent over the last decade.

In the last month, its task became much more complicated.

The United States has enacted sweeping sanctions on Russia in response to its invasion of Ukraine, freezing the assets of its central bank, blocking transactions associated with major financial institutions and targeting top government officials and oligarchs. Experts consider the sanctions to be the most robust ever directed at a major economy, but they are also expected to spur aggressive evasion measures by Russians.

I.R.S. officials said they would use financial tracing technology and work with banks and international counterparts to track how oligarchs and others were shifting money and assets around the world in violation of the sanctions. They are looking for signs of newly created fictitious businesses that could be used to shelter assets and transactions involving cryptocurrencies, which criminals use to move money anonymously.

According to the report, the I.R.S. seized $3.6 billion of stolen cryptocurrency last year and has already surpassed that this year.

Finding support for more money for the I.R.S. will not be easy. An agency official said Republicans had blocked a request for more criminal investigation funds in the spending bill that Congress passed last week.

Mr. Rettig will make the case personally on Thursday morning when he testifies before the House Ways and Means Committee.

“A strong, robust criminal tax enforcement presence provides significant deterrence to those willing to evade their lawful obligations to our country,” Mr. Rettig will say, according to a copy of his prepared remarks. “Without adequate resources, we risk sending a much less powerful message to would-be and active tax evaders.”