The Obama administration marked with little fanfare a major milestone in its bank rescue effort  its decision on Tuesday to let 10 big banks repay federal aid that had sustained them through the worst of the crisis  as policy makers and industry executives focused on the challenges still before them.

“This is not a sign that our troubles are over,” President Obama said. “Far from it.”

While the announcement had been expected for weeks, the official word put the administration’s imprimatur on a corps of big banks considered healthy enough to extricate themselves from Washington’s grip.

The bank holding companies, among them American Express, Goldman Sachs, JPMorgan Chase and Morgan Stanley, plan to return a combined $68.3 billion. That represents more than a quarter of the federal bailout money that the nation’s banks have received since last October, when many feared that failures might cascade through the industry.

But the decision to allow the banks to exit the Troubled Asset Relief Program, or TARP, also ushered in a new, and potentially risky, phase of the banking crisis. Letting the lenders out now  earlier than many had envisioned, and without the industry reforms some consider necessary to prevent future crises  raises many sobering questions for policy makers, bankers and taxpayers.