American banks and corporations claiming billions of dollars in unpaid debts from the Iranian government have gone to court to establish claims to Iranian assets frozen here, positioning themselves for the time those assets are freed.

In New York City last Thursday a federal judge granted an order of attachment for $366 million claimed by Chase Manhattan Bank, and in U.S. District Court here late Friday evening, another judge granted a temporary restraining order barring Iran from removing or concealing any of its assets in the United States pending determination of the claim of a group of insurance companies for about $35 million.

Those are just two of more than 60 such claims filed around the country seeking a judicially imposed temporary hold on Iranian assets on top of President Carter's order of Nov. 14 blocking Iranian assests in the U.S.. Most of the actions have been filed in New York, where the majority of Iran's assets are frozen.

"We're getting copies of new suits everyday," said Thomas G. Shack Jr., whose firm, Abourezk, Shack & Mendenhall, has represented the Iranian government in several proceedings.

Shack said some of the suits go beyond the president's order, seeking to attach assets that under the executive freeze might be used for food purchases and other transactions with Treasury approval.

In general the actions claim money owed for loans in defalut or for breach of contract such as unpaid bills or failure to pay for equipment that companies claim to have been unable to get out of Iran.

The insurance companies' claim is for money owed for assets nationalized by Iran.

Such actions "could make it very difficult for the Executive [Branch] to deal with the freeze as a political issue," said Shack. "If the president wanted to withdraw the freeze as part of a political solution," the private actions might arguably render that action less meaningful, he said.

Several orders of attachment have been granted in New York, where under state law they are honored in the order in which they are filed, according to several attorneys. If confirmed in later court hearings, the orders would become meaningful only after the companies' were litigated or otherwise settled and only after the assets were unblocked.

On the other hand, according to attorneys familiar with the case and to Treasury Department spokesmen, another followup to the end of the freeze might be claims legislation by Congress which would divide up the assets on hand.

For now, legal actions "can't lead to judgement against the frozen assets,' said a Treasury spokesman. "As long as the freeze continues, the assets are preserved for all claimants."

Other banks filing claims in New York include Manufacturers Hanover Trust Co. for $84 million, Morgan Guaranty Trust Co. for $86 million, First National Bank of Boston, Bankers Trust Co. and Chemical Bank and Trust Co. Iran announced on Nov. 23 that it would refuse to honor some foreign debts.

Corporations staking claims against Iran include companies that have supplied oil-drilling equipment and operations, and other firms, including Starrett Housing Corp., Lockheed Corp., Du Pont Co. and American Express.