The bill aims to bring Iran's laws in line with international standards and allow it to join the UN Terrorism Financing Convention.
It is one of four bills put forward by the government in recent months in a bid to meet demands by the international Financial Action Task Force (FATF), which has given Iran until later this month to tighten its laws against money laundering and terror financing.
"Neither I nor the president can guarantee that all problems will go away if we join (the UN convention)," said Iran's Foreign Minister Mohammad Javad Zarif during Sunday's debate.
"But I guarantee that not joining will provide the US with more excuses to increase our problems," he added.
The issue has become particularly pressing since the United States walked out of the 2015 nuclear deal with Iran earlier this year and began reimposing sanctions.
The other parties to the deal -- Britain, France, Germany, China and Russia -- have sought to salvage the agreement and maintain trade with Iran, but have demanded that it accede to the FATF.
Joining the UN convention has been controversial because hardliners say it will limit Iran's ability to support armed groups in the region such as its Lebanese ally, Hezbollah.
Iran is alone with North Korea on the blacklist of the FATF, although the Paris-based organisation has suspended counter-measures since June 2017 while Iran works on reforms.
A previous bill on the mechanics of monitoring and preventing terrorist financing was signed into law in August.
Two other bills -- on money-laundering and organised crime -- have also been passed by parliament but have been delayed by higher authorities that vet legislation, including the Guardian Council.
'Death to traitors'
Conservatives were furious after Sunday's bill passed by 143 votes to 120, with protesters chanting "death to traitors" outside parliament.
In a heated debate ahead of the vote, opponents of the bill said it would not solve the country's financial problems, and would help its enemies.
Hardline lawmaker Mohammad Dehghan warned the bill means "providing the enemy with intelligence during an economic war" and that passing it amounted to "treason".
Economists say greater transparency could cause problems for powerful behind-the-scenes networks, including the Revolutionary Guards military organisation, which is deeply embedded in Iran's opaque economy.
Both sides of the debate have evoked supreme leader Ayatollah Ali Khamenei to support their position.
Conservatives pointed to Khamenei's statement in June that Iran has "no need to join" global conventions.
But parliament speaker Ali Larijani, who supports the government's position, said he had received a letter from Khamenei explaining that his remarks were about "conventions in general" and not meant to oppose any particular bills.
Reformist lawmaker Mohammad Feyzi told the session that Iran does not have "the luxury of choice" and will face negative consequences if it refuses to join the FATF.
Ali Najafi, spokesman for the parliament's commission which produced the bill, said Iran retained the right to walk away from the UN convention "wherever it acts against the Iranian constitution" and emphasised that it does not force Iran to recognise Israel.
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