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PARIS - Their relationship already heavily burdened by the Iraq war, the Israeli-Palestinian conflict and the solution to global warming, the last thing that Europe and the United States need is a squabble over Iran.
But a bustup could be in the offing, for the two sides are following familiarly divergent paths as a deadline looms for tightening punishment against Iran for uranium enrichment.
On Sunday, as Iranians were called to mass rallies for the 28th anniversary of the Islamic Revolution, diplomats at the Conference on Security Policy in Munich, Germany, were struggling for a temporary fix that would stop the enrichment programme, save Iran's face and avert a transatlantic row.
On February 21, the head of the International Atomic Energy Authority (IAEA), Mohamed ElBaradei, is to report on Tehran's compliance with demands set out in a United Nations Security Council resolution in December. That resolution adopted sanctions against Iranian individuals and companies linked to the nuclear and ballistic missile programmes.
Instead of halting the enrichment, the Islamic republic is gearing up from research to full-scale production. It insists that the programme is only to generate power.
US President George W. Bush is doing what he can to press Europe into toughening its line. He is rattling the sabre, dispatching a second aircraft carrier group to the Gulf, deploying Patriot anti-missile defences to the region and warning Iran over any support to Iraqi insurgents.
The second prong to Bush's strategy is to lobby for the Europeans to follow the US in choking off trade and economic ties with Iran.
The US chief delegate to the IAEA, Gregory Schulte, last week chided Europe.
"Faced by the defiance of Iran's leadership, the European Union and European countries can do more - and should do more - to bolster our common diplomacy," said. "Why, for example, are European Governments using export credits to subsidise exports to Iran? Why, for example, are European Governments not taking more measures to discourage investment and financial transactions?"
This manoeuvering and sermonising has gone down badly in European capitals. Unlike in the US, there are no laws or regulations in Europe barring business with Iran, except where stipulated in the UN resolution.
It also irks Europeans that the US singles them out rather than Russia, one of the architects of the Iranian nuclear programme.
The US measures "have no effect for the European people", French Foreign Ministry spokesman Jean-Baptiste Mattei said.
"Nobody in Europe is going to give up the opportunity of doing business with Iran just for the sake of pleasing the Americans," said an oil consultant, pointing to the profits that can be made by petroleum majors.
The European position, though, is not monolithic. Britain, predictably, is aligned with the US. Germany, which holds the presidency of the European Union as well as the year-long chair of the G8 nations, wants diplomacy.
Last week, during a visit to Kuwait, German Chancellor Angela Merkel said a "military option" against Iran was out of the question.
France, unlike in the runup to the Iraq War, is demanding firmness but is worried by the US approach.
"We must show Iran that firstly it has more to lose than gain from an enrichment programme that worries the international community, but also that if Iran accepts to respect its international obligations, it has much more to gain that lose," French Prime Minister Dominique de Villepin said last week.
"We must combine dialogue with firmness in our approach. I think the US and Europe can go further in dialogue and proposals."