Federal prosecutors in Chicago and New York have issued subpoenas in the probe of the collapse of MF Global Holdings Ltd., people familiar with the case said, a sign of an intensifying Justice Department criminal investigation as authorities try to track down about $600 million in client funds.

Chicago U.S. Attorney Patrick Fitzgerald and New York U.S. Attorney Preet Bharara, regarded as two of most aggressive and high-profile federal prosecutors in the country, are using subpoenas to gather company records, the people familiar with the matter said.

The Justice Department and the FBI are conducting a criminal investigation of MF ...