The United Emblem, which is carrying more than 1 million barrels of oil, is one of three tankers loaded with oil from the autonomous Kurdish region, which is trying to sell oil independently.
Iraqi Kurdistan is locked in a bitter legal and diplomatic struggle with Baghdad over international oil sales.
A US judge on Tuesday refused a request by Baghdad, citing a lack of jurisdiction, to seize 1 million barrels of oil aboard the United Kalavrvta tanker, which has been anchored off the port of Galveston since the weekend.
The Kurdistan Regional Government filed a letter with the Texas court arguing its sales are allowed under the Iraqi constitution.
Another tanker carrying Kurdish oil, the United Leadership, has been anchored off Morocco for almost two months.
All three tankers are managed by Marine Management Services MC, a Piraeus-based shipping company.
A senior executive at Marine Management Services confirmed the ship-to-ship transfer involving the United Emblem took place in a "legitimate operation".
The ship is "fixed to a legitimate charterer and performing legitimate operations," said Kostas Georgopoulos, the chartering manager at Marine Management Services.
"The ship is still in international waters," he added.
Georgopoulos declined to name the charterer or the details of the oil transfer but was aware the 161,724 dwt (deadweight tonne) ship was carrying oil from Iraqi Kurdistan.
Around half of the ship's cargo could have been offloaded, according to Reuters AIS ship tracking data.
Data on July 28 showing the ship was anchored with a 100 percent draft indicated the tanker was fully loaded. The ship's draft was 74 percent of the maximum when the information was updated on Thursday, compared with around 60 percent if the tanker was empty.
The ship is anchored in the South China Sea about 20 km off the east coast of Peninsular Malaysia and about 50 km north-east of Singapore, Reuters data showed.
Georgopoulos did not know where the ship was headed next, saying the charterers were controlling the vessel.
"It's not us controlling the tanker. We are expecting the issuing of orders," Georgopoulos said.
The London based insurer of the ship, the London P&I Club, declined to comment specifically on the vessel or its cargo, although director Steve Roberts, said: "We have had some contact" with Marine Management Services.
The United Emblem loaded the oil cargo at Ceyhan in Turkey in mid-June, according to Reuters data, although exports have now stopped because storage at the port is at capacity forcing the Kurdistan Regional Government to shut-off its pipeline.
The United States has publicly opposed direct oil sales, fearing they could contribute to the break-up of Iraq, and instead believes Baghdad and the Kurdistan Regional Government should reach an agreement on how the proceeds from oil sales should be split.
BA/BA