After First Republic Bank's disappointing earnings and potential asset sale rekindled fears that the banking crisis has not ended, US stocks fell the most in two months, and Treasury yields fell.

The S&P 500 fell 1.6% on Tuesday, with First Republic's stock plummeting 49% to a record low. According to reports, the troubled bank, which saw higher-than-expected withdrawals in the first quarter, is considering selling up to $100 billion in long-term mortgages and securities as part of a larger rescue plan.

As investors sought the safety of US government debt, the two-year Treasury yield fell to 3.93%. Meanwhile, tech stocks rose in after-hours trading, led by Microsoft and Alphabet, which reported better-than-expected earnings.

The Federal Reserve is still expected to raise interest rates by a quarter percentage point when it meets next week, despite signs that the American economy is slowing after a year of aggressive tightening. Tuesday's data showed a drop in consumer confidence, while two regional Fed manufacturing reports disappointed.