LONDON—British bank Barclays PLC unveiled plans Tuesday to increase its capital levels by nearly $20 billion, one of the boldest recent attempts by a European bank to put to rest questions about its financial strength.

Even as Barclays addressed one of regulators' main concerns about the bank, however, a new problem emerged: A British regulatory agency is planning an enforcement action against the bank over a 2008 fundraising deal with Qatari investors, people familiar with the probe said.

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