PANAMA CITY, March 24 (Reuters) - A unit of Hong Kong conglomerate CK Hutchison ( CKHUF ) said on Tuesday it had widened its claims in an international arbitration case against Panama, saying damages had now risen to more than $2 billion.

Panama Ports Company, which for nearly three decades operated the Balboa and Cristobal terminals near the Panama Canal, said it had supplemented its claims in proceedings under the International Chamber of Commerce's arbitration rules, a month after what it described as the state's illegal takeover of two port terminals and company property.

Panama's presidency and maritime authority did not immediately respond to requests for comment.

The legal fight has become part of a broader diplomatic and commercial dispute following Panama's cancellation of the concessions in line with a Supreme Court ruling in late February.

The cancellation followed mounting U.S. pressure to curb Chinese influence around the strategic canal, which handles about 5% of global maritime trade.

Panama Ports Company (PPC) has accused Panamanian authorities of unlawfully seizing property, confiscating private and protected documents and denying the company access to files and computers during and after the takeover of the facilities.

The company added on Tuesday that Panama had continued a campaign against the firm and failed to coordinate property access or compensation.

Earlier this month, PPC alleged Panama missed a March 13 deadline to respond in the arbitration case, because it did not have proper legal representation.

Panamanian President Jose Raul Mulino said accusations over setbacks in the arbitration process were "outrageous" and "a lie." Mulino said the government had appointed international counsel to defend the state's interests.

The dispute has also complicated CK Hutchison's ( CKHUF ) planned $23 billion sale of a majority stake in its global ports business to a consortium led by BlackRock and Mediterranean Shipping Company (MSC). The company said this month it remained in talks over the transaction.

Panama has granted temporary 18-month concessions to keep the terminals operating, with APM Terminals managing Balboa and TIL Panama, a unit of MSC, handling Cristobal.