BRUSSELS—The European Commission will do everything to avoid a run on Italian banks following the turmoil in global markets spurred by the U.K.'s vote to leave the European Union, commission President Jean-Claude Juncker said Tuesday.

Speaking at the end of a summit of EU leaders here, Mr. Juncker said he discussed the state of Italian banks with Italian Prime Minister Matteo Renzi, and that the bloc must make sure that the banking sector in Italy and elsewhere is well protected.

"The commission will do everything to avoid any kind of bank run," Mr. Juncker said. "This is not a danger for Italy for now but we have to make sure given the uncomfortable global circumstances we are in that the banking sector in Italy and elsewhere will be protected in the best way possible."

His comments come as the Italian government is considering a capital injection for the country's banking system, according to people familiar with the matter, after Italian lenders were hit by a sharp selloff in banking stocks Friday, triggered by Britain's vote to leave the EU.

The intervention could add up to €40 billion in capital to the banking sector, one of the officials said, which is struggling under the weight of €360 billion in bad loans, chronically poor profitability amid record-low interest rates, thin capital buffers and high costs.

The aftershocks of the U.K.'s vote to leave the EU in a referendum earlier this month have rattled financial markets, sending European banking shares lower.

Earlier Tuesday, European Central Bank President Mario Draghi told EU leaders that he expects the U.K.'s decision to exit the European Union to reduce economic growth in the eurozone by up to 0.5% over three years, people familiar with the matter said.

The economic hit is the result of the U.K.'s importance as a major trading partner, and a possible perception that the EU could become ungovernable, the people said.

Giovanni Legorano contributed to this article.

Write to Viktoria Dendrinou at viktoria.dendrinou@wsj.com and Laurence Norman at laurence.norman@wsj.com

(END) Dow Jones Newswires

June 28, 2016 21:25 ET (01:25 GMT)