Companies around the world are drawing down their credit lines at the same time, forcing banks to cough up large sums of money on short notice and further straining a financial industry already hammered by sinking interest rates.

The pressure on banks was highlighted by a rare and dramatic Sunday evening move by the Federal Reserve, which cut its benchmark interest rate by a full percentage point to almost zero and took a range of actions to support bank lending, including flooding markets with liquidity by ratcheting up its...