JPMorgan, the nation's largest bank, told all employees they "should never give the appearance of exploiting a situation of stress or uncertainty," in a March 13 memo, extracts of which were seen by Reuters. "We do not make disparaging comments regarding competitors."

On the same day, the leaders of its consumer and business banking unit told branch employees: "We should refrain from soliciting client business from an institution in stress," according to extracts seen by Reuters.

Citigroup has also given similar guidance to its business heads, a source familiar with the matter said. The guidance includes not speculating about other banks or market rumors. The bank runs that toppled Silicon Valley Bank (SVB) and Signature Bank, the second and third largest lenders to fail in U.S. history, prompted customers to move about half a trillion dollars of deposits from the "most vulnerable" U.S. banks to bigger institutions this month, JPMorgan analysts led by Nikolaos Panigirtzoglou wrote in a note Wednesday.

As SVB teetered, billions of dollars in deposits poured into the nation's banking giants, which are required by regulators to hold more capital to withstand shocks. While lenders regularly compete for customers, the loss of confidence that shook the banking system in the last two weeks sparked concerns about contagion that could lead to a broader panic.

The turmoil prompted unprecedented moves by regulators to guarantee the deposits of SVB and Signature. President Joe Biden, Treasury Secretary Janet Yellen and Citigroup Inc. Chief Executive Jane Fraser have all made statements in recent days to reassure the public that the U.S. banking system is safe.

"We all have a vested interest in keeping America's financial system strong and thriving," a JPMorgan spokesperson said. "It's the envy of the world with thousands of institutions of all sizes serving every corner of the country."

(Reporting by Lananh Nguyen and Saeed Azhar in New York; editing by Megan Davies and Jonathan Oatis)

By Lananh Nguyen and Saeed Azhar