The latest step is part of a wider array of sanctions the White House plans to announce on Thursday to make Russia pay a price for "malign" actions such as election interference, cyber-hacking, the use of chemical weapons and reports that it offered Taliban militants bounties to kill US soldiers in Afghanistan.
The prospect of losses for US banks, following hedge fund Archegos Capital's default on margin calls, also had market participants concerned.
US money market funds received a net $50.35 billion in the week to March 31, after an over $60 billion inflow in the previous week, data from Refinitiv Lipper showed.
JPMorgan Chase & Co, Bank of America Corp and Citigroup took in more than $1 trillion in deposits last year, compared with a $92 billion increase in 2019.
Big banks will not shun deposits due to the dynamic, executives said, because doing so could hurt their franchises.