The move came as authorities in the US are trying to quell panic over the health of the banking system, after a series of bank collapses in the US.
BBC reports worries about the sector have spread globally, raising fears of a crisis.
US regulators called the move "most welcome", while the banks said their action reflected their "confidence".
They said the banking system had plenty of cash and made big profits.
"Recent events did nothing to change this," they said. "The actions of America's largest banks reflect their confidence in the country's banking system."
Reports of plans for the aid from the 11 banks, led by JP Morgan and Citigroup, helped lift financial markets and sent shares in First Republic surging more than 20% at one point, triggering trading halts.
But a sell-off started again in after-hours trade in a sign that concerns remain.
The San Francisco-based firm had seen its share price plunge nearly 70% over the last week, as investors worried it was the next bank at risk of a rush of customers withdrawing their deposits.
"This show of support by a group of large banks is most welcome, and demonstrates the resilience of the banking system," US financial officials said.