Last year, Malaysia's CIMB Group Holdings and RHB Bank sent closure notices to many Iranian clients, a sign that U.S. sanctions were having far-reaching effects on citizens of the Islamic republic.

Former Malaysian Prime Minister Mahathir Mohamad, after a Reuters story on the closures, said his government was forced to "make it difficult" for Iranians living in the Southeast Asian country.

Maybank has since January offered Iranians local debit cards that do not carry the usual Visa or MasterCard logos, meaning they are not meant for international transactions, many of those receiving the cards have told Reuters.

"It is issued to enable this group of customers to carry out banking and everyday transactions conveniently, and not be confined solely to branch services," a Maybank spokesman said.

The spokesman did not explain the restrictions on usage of the cards. Previously, several Iranians have said that they were told by Maybank that they would not be able to replace or renew debit or credit cards if those went missing or expired.

CIMB told its Iranian customers last August it was going to shut their banking accounts, without giving any reason. However, some Iranians are still able to access their accounts online, checks by Reuters found.

Network engineer, Amir Nazari Mehrabi, for instance, said he could still access his CIMB account but was not confident of using it.

He recently started banking with Maybank and said the special card has been helpful.

"Imagine, every time I had to go to the bank with my passbook and passport. It's silly. I would prefer CIMB but I am really afraid to keep a lot of money there," he said.

CIMB told Reuters its operations of its customers' banking accounts, foreign and local, were in compliance with local and international regulatory requirements.

RHB declined to comment.

By Liz Lee