BP wants the court to award the oil giant damages against Cameron and to declare that the device maker caused or contributed to the disaster and is responsible for some or all costs incurred by BP.
Eleven people were killed when the Deepwater Horizon rig exploded on April 20, 2010, leading to more than 200 million gallons (757 million liters) of oil spewing from an undersea well.
A testing firm hired by the government determined last month the blowout preventer had a faulty design. But it also cited other problems related to rig crew actions.
BP said in a statement that it wants Transocean to pay its "proportionate" share of all damages and liabilities from the disaster. A Transocean spokesman did not immediately respond to an email seeking comment.
Houston-based Cameron noted in a statement emailed to AP that Wednesday was the deadline under the relevant statute for all parties to file claims against each other.
"It is not surprising that the companies are filing to protect their indemnity rights (except in the case of BP) and whatever claims they believe they have," Cameron said. "Additionally, in order to protect ourselves, we, too, have filed crossclaims and counterclaims, including our indemnity claims, against other parties to the litigation."
Cameron, one of the largest makers of blowout preventers, has defended the integrity of its devices and workmanship.
Also Wednesday, Transocean filed court papers demanding that judgments be made against BP, Cameron and other companies in its favor. Among other things, Transocean wants a judgment against BP for $12.9 million and a judgment against cement contractor Halliburton and other companies for $20 million.
Transocean said the figures stem from contractual obligations and the money it lost when the rig sank.
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