U.S. oil producer ConocoPhillips Co. (NYSE: COP) is far from collecting the full value of a $2 billion arbitration award against Venezuelan state oil company PDVSA , ConocoPhillips' CEO said May 15.

ConocoPhillips has won court orders allowing the company to begin seizing PDVSA assets in efforts to collect on an award by the International Chamber of Commerce over the 2007 nationalization of its projects in Venezuela.

While ConocoPhillips started seizing assets this month, CEO Ryan Lance is telegraphing that the company intends to escalate its campaign against PDVSA across the globe as it works to recoup losses. That threatens to further limit revenue at the state-controlled firm, the single largest moneymaker for the OPEC member.

"It's not close to the $2 billion today, but over time we expect to be able to recover it," Lance said at ConocoPhillips's annual shareholder meeting in Houston. "We're just trying to look where all the assets are."

ConocoPhillips has filed with courts in the U.S., Hong Kong, the U.K. and throughout the Caribbean in an attempt to begin the legal process of seizing additional PDVSA assets, Lance said.

ConocoPhillips on May 15 moved to seize at least two cargoes of crude and fuel near a terminal operated by PDVSA subsidiary Citgo Petroleum in Aruba, sources told Reuters.

In Asia, PDVSA is co-owner with PetroChina of CV Shipping Pte Ltd., a Singapore-based tanker operator, according to CV Shipping's website. The joint venture has four tankers, each capable of transporting 2 million barrels of oil.

In Europe, PDVSA is a co-owner with Finland's Neste Corp. of AB Nynas Petroleum, according to PDVSA's website. The joint venture, which processes about 30,000 barrels of crude per day, operates two U.K. refineries.

ConocoPhillips has had early success in asset seizures in some Dutch regions of the Caribbean due to specific legal statutes, though other jurisdictions are expected to take longer, Lance said.

The moves have disrupted fuel deliveries throughout the Caribbean, much of which depend on PDVSA. Aruba's prime minister, Evelyn Wever-Croes, told journalists on May 15 that the situation with ConocoPhillips in the Caribbean is worrisome.

"We're trying to minimize any impact that this might have on the islands in the Caribbean," Lance said. "We are concerned about putting them in the middle of this thing, between PDVSA and ourselves."

Three Curacao state-run utilities said May 15 they were filing suit in a local court to determine the responsibility of the local Isla refinery, operated by PDVSA, to meet fuel supply contracts following ConocoPhillips' efforts to attach assets there.

The utilities, which include power and water company Aqualectra and fuel distributor Curoil, said a lack of fuel could have a severe impact on their operations and therefore on the local population.

PDVSA, which operates Isla, has stopped sending crude shipments on concern they could be attached.

Houston-based ConocoPhillips has two other outstanding arbitration awards against PDVSA.