The significantly undercapitalized Amcore Financial Inc. is warning that its bank might fail if it cannot come up with an acceptable capital plan within a few weeks.

The $4.4 billion-asset Amcore said in a Securities and Exchange Commission filing late Monday that regulators rejected a previously submitted plan and gave it until Dec. 4 to submit a new one.

The plan must detail how it intends to boost its capital ratios or sell itself, otherwise the regulators might take further action, including seizing its bank, the filing said.

In the third quarter, Amcore reported a loss of $156.4 million.

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