The bill, one of four put forward by the government to meet demands set by the international Financial Action Task Force (FATF), was passed by 143 votes to 120, according to the semi-official ISNA news agency.
It aims to bring Iran's laws in line with international standards and allows it to join the UN Terrorism Financing Convention.
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"Neither I nor the president can guarantee that all problems will go away if we join (the UN convention)," said Foreign Minister Mohammad Javad Zarif during the debate ahead of the vote.
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"But I guarantee that not joining will provide the US with more excuses to increase our problems," he added.
Iran is currently alone with North Korea on the blacklist of the FATF, which monitors global money laundering and terrorist financing.
In June, the Paris-based FATF gave Iran three months to pass laws needed to be removed from the blacklist, which has added to the Islamic republic's woes in accessing global banking.
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