CARACAS -- Worries grew Thursday that Venezuela is on the verge of a banking crisis, causing a run on smaller lenders, sinking the country's currency and bond prices, and stoking fears that president Hugo Chávez could nationalize the banking system.

Venezuelans and investors are concerned about small banks' solvency following this week's seizure of four banks run by a billionaire close to the government of President Chávez. The populist leader may have fanned the fire when he assured Venezuelans twice this week that he stood...