Potential fault lines surfaced on Tuesday over whether the Federal Reserve should proceed with interest rate increases next month as it studies the fallout from banking-sector stresses triggered by the collapse of two midsize banks last month.

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Chicago Fed President Austan Goolsbee said the central bank should proceed cautiously with any additional rate rises as it assesses after-effects of the bank failures during a speech Tuesday. “At moments like this of financial stress, the right monetary approach calls for prudence and patience,” he said in a speech at the Economic Club of Chicago.