Big banks’ demand for longer-term Federal Reserve liquidity flared up again on Tuesday, on a day where the central bank extended its plans to intervene in markets into mid-February.

The Federal Reserve Bank of New York said it intervened twice via repurchase agreements, or repos. Eligible banks drew $47 billion in overnight liquidity from the central bank, less than the $120 billion the Fed was willing to provide. But the 14-day repo saw banks offer the Fed $43.2 billion in securities, against the Fed’s $35 billion cap. Collectively,...