A group of Lloyd's syndicates, led by Syndicate 741, is being sued for $6m (£3.3m) by the National Iranian Tanker Company (NITC).
The dispute relates to NITC's losses as a result of damage to its vessels, the Iran Noah, the Iran Nesa and the Iran Nabi.
NITC said the syndicates, along with several other non-Lloyd's insurers, agreed to insure the company against damage to the vessels caused by "bursting of boilers, breakage of shafts, or any latent defect in the machinery or hull".
According to NITC, cracks were discovered in the three vessels in April 2000.
NITC subsequently made claims to its insurers, led by Syndicate 741, in relation to the damage to the three vessels. NITC claimed there was about $2m (£1.1m) of damage to each vessel.
NITC said: "In breach of the terms of the insurances, the defendants have failed to indemnify NITC for their losses."
A spokesman for Syndicate 741 said it would be "inappropriate to comment" on the dispute as legal proceedings were underway.
Other defendants named in the suit include Arig Insurance Company, Chevanstell and London & Edinburgh Insurance.