Two-dozen crew members aboard a Danish ship seized by Iran in the Strait of Hormuz last month could soon be free after the vessel's owner agreed to pay $163,000 to settle a decade-old legal dispute, officials said Wednesday.

Iranian forces boarded the Maersk Tigris on April 28 after firing warning shots across the container ship's bridge, and guided it to its present mooring off the Iranian coast near the port of Bandar Abbas. Although Iran insists the crew members, mostly Eastern European and Asian sailors, are not being detained, they appear to be stranded aboard the ship while an Iranian court rules on the dispute.

"We must insist that the crew and vessel are released as soon as possible."

- Statement from shipping giant Maersk

"We must insist that the crew and vessel are released as soon as possible," international shipping giant Maersk said in a statement. "The crew is not employed by Maersk Line, nor is the vessel owned by Maersk Line. Maersk Tigris and its crew are thus not in any way party to the case."

Maersk chartered the ship, which is operated by Singapore-based Rickmers Ship Management and owned by undisclosed private investors. Maersk said Wednesday it had agreed to pay an Iranian company $163,000 after an Iranian court ruling in February that related to a dispute about 10 container boxes transported from Iran to Dubai in 2005. The containers were transported aboard a Maersk ship, but discarded after going unclaimed for 90 days.

Maersk claims that since it does not own the Tigris, the seizure has no lawful connection to the dispute.

An Iranian appeals court on April 30 ordered Maersk to pay $3.6 million to resolve the dispute, but Maersk spokesman Michael Christian Storgaard told Fox News Wednesday the company has agreed only to pay a $163,000 fine imposed by an Iranian court in February.

“We are not discussing $3.6 million,” Storgaard said.

Although Iranian officials have repeatedly said the vessel will not be released until the case is settled, which would seem to mean full payment of the judgment, Iranian foreign ministry spokeswoman Marzieh Afkham said Wednesday after Maersk agreed to pay the fine that the matter could be settled soon.

"Negotiations are continuing with the private company that has filed the complaint and with the other party, and it is possible that this case will be resolved in one or two days," she said.

When asked why Maersk was not demanding the unconditional release of the ship by Iran, Storgaard said Maersk had tried that, but was now opting for Plan B.

“We have done that all the time [asked for the Maersk Tigris to be released], but now we are now asking, ‘how can we solve this?’” he said.

The incident occurred at a critical juncture in U.S.-Iranian relations, which could thaw after decades of hostility should a tentative nuclear deal between Tehran and six world powers including Washington be clinched. It also coincided with heightened tension between regional arch-rivals Iran and Saudi Arabia over the civil war in Yemen, in which they support opposing sides.

U.S. Navy ships began accompanying U.S.-flagged commercial vessels through the Strait of Hormuz on April 30. Iranian ships shadowed the U.S.-flagged Maersk Kensington on April 24.

Fox News’ Lucas Tomlinson, Reuters and The Associated Press contributed to this report.