AIX-EN-PROVENCE, France/LONDON, July 7 (Reuters) - One of the world’s biggest cargo shippers announced on Saturday it was pulling out of Iran for fear of becoming entangled in U.S. sanctions, and President Hassan Rouhani demanded that European countries to do more to offset the U.S. measures.

The announcement by France’s CMA CGM that it was quitting Iran deals a blow to Tehran’s efforts to persuade European countries to offer economic benefits to offset the new U.S. sanctions.

Iran says it needs more help from Europe to keep alive an agreement with world powers to curb its nuclear programme. U.S. President Donald Trump abandoned the agreement in May and has announced new sanctions on Tehran. Washington has ordered all countries to stop buying Iranian oil by November and foreign firms to stop doing business there or face U.S. blacklists.

European powers which still support the nuclear deal say they will do more to encourage their businesses to remain engaged with Iran. But the prospect of being banned in the United States appears to be enough to persuade European companies to keep out.

Foreign ministers from the five remaining signatory countries to the nuclear deal -- Britain, France, Germany, China and Russia -- offered a package of economic measures to Iran on Friday to compensate for U.S. sanctions that begin taking effect in August, but Tehran said the package did not go far enough.

“European countries have the political will to maintain economic ties with Iran based on the JCPOA (the nuclear deal), but they need to take practical measures within the time limit,” Rouhani said on Saturday on his official website.

CMA CGM, which according to the United Nations operates the world’s third largest container shipping fleet with more than 11 percent of global capacity, said it would halt service for Iran as it did not want to fall foul of the rules given its large presence in the United States.

“Due to the Trump administration, we have decided to end our service for Iran,” CMA CGM chief Rodolphe Saade said during an economic conference in the southern French city of Aix-en-Provence.

“Our Chinese competitors are hesitating a little, so maybe they have a different relationship with Trump, but we apply the rules,” Saade said.

The shipping market leader, A.P. Moller-Maersk of Denmark, already announced in May it was pulling out of Iran.

In June, French carmaker PSA Group suspended its joint venture activities in Iran, and French oil major Total said it held little hope of receiving a U.S. waiver to continue with a multibillion-dollar gas project in the country.

Iranian Oil Minister Bijan Zanganeh called the tension between Tehran and Washington a “trade war”. He said it had not led to changes in Iranian oil production and exports.

He also echoed Rouhani’s remarks that the European package did not meet all economic demands of Iran.

“I have not seen the package personally, but our colleagues in the foreign ministry who have seen it were not happy with its details,” Zanganeh was quoted as saying by Tasnim news agency.

Some Iranian officials have threatened to block oil exports from the Gulf in retaliation for U.S. efforts to reduce Iranian oil sales to zero. Rouhani himself made a veiled threat along those lines in recent days, saying there could be no oil exports from the region if Iran’s were shut.

Zanganeh said Iran’s stance on this issue was clear. (Reporting by Bozorgmehr Sharafedin, Leigh Thomas and Sarah White Editing by Peter Graff)