As debate rages among politicians and pundits in Washington over whether to endorse last month’s historic nuclear compromise with Iran, key European allies have already given their verdict: a resounding thumbs up.

Government ministers and business leaders in France, Germany, Italy and elsewhere in the EU are racing to open up a new era of diplomatic, trade, investment and possible future military cooperation with Tehran, regardless of what American and Israeli sceptics say.

While Americans argue over timescales, technicalities and Iranian trustworthiness, behind their backs the scramble for Persia, recalling Europe’s 19th-century scramble for Africa, has already begun. The cohesion of the international sanctions regime isolating Iran is crumbling by the day.

Barack Obama is fighting hard to win congressional approval for the nuclear agreement. In a speech on Wednesday marking the 1945 atomic bombing of Hiroshima and the anniversary of the 1963 nuclear test ban treaty, he is expected to suggest that his opponents are the same people who supported the ill-fated 2003 Iraq invasion. The implication is clear: if the deal is shot down, another Middle East war may soon follow.

“It’s now more than 50 years since President Kennedy stood before the American people and said, ‘Let us never negotiate out of fear, but let us never fear to negotiate’,” Obama said last month. The Iran agreement, he added, was the product of “smart, tough diplomacy”.

Binyamin Netanyahu, Israel’s prime minister, is leading the rejectionist charge, backed by well-funded lobbyists such as the American-Israel Public Affairs Committee. In a US webcast on Tuesday he said the pact, which envisages billions of dollars in sanctions relief for Iran, was a bad deal encouraging nuclear weapons proliferation.

“The nuclear deal doesn’t block Iran’s path to the bomb. It actually paves Iran’s path to the bomb,” Netanyahu said. Obama’s claim that opponents favoured war was “utterly false”.

In the event of defeat in next month’s vote in Congress, White House officials say they have enough Democratic votes to sustain a presidential veto, enabling the pact to go through. But there may also be attempts to block it at state level. Because the deal is an “executive agreement”, not a treaty, constitutional experts say state assemblies have the right to debate and reject it.

While America wrangles, European countries, encouraged by a unanimous UN security council endorsement, are busily mending fences with Iran, keen not to miss out on potentially mouth-watering financial, trade and geopolitical dividends.

Although implementation of the deal is staggered, they are acting as though sanctions have already been lifted. They have not. But it seems increasingly plain that, even if Congress blocks Obama, it may be too late to rescue the international sanctions regime.

Harvard analyst Stephen Walt said: “In the end, we either implement this deal, or we will have: 1) a collapse of the sanctions regime and an Iran that is free to develop its nuclear capacity with few constraints, or 2) a preventive war that would give Iran a powerful incentive to acquire a bomb and only reduce its capacity to do so temporarily.’’

Signs of unravelling are everywhere. Making the first visit to Iran by a French foreign minister for 12 years, Laurent Fabius said last month that France hoped to cash in on business opportunities, especially oil and cars. A delegation of about 100 French business leaders will visit Tehran in September. In a dramatic gesture of renewed friendship, Fabius said Hassan Rouhani, Iran’s president, had been invited to make a state visit to France in November.

An Iranian government spokesman, Mohammad-Bagher Nobakht, said Fabius’s visit could open the way for the sale to Iran of French-made Mirage warplanes, a development that may alarm the Pentagon and Gulf states hostile to Iran.

Others have not been far behind. Sigmar Gabriel, Germany’s vice-chancellor and economy minister, met Rouhani in Tehran last month in an effort to get in early. A delegation of German business representatives also travelled to Iran, including the heads of the industrial gases group Linde and the chemicals firm BASF. A preliminary agreement to open German banks in Iran has reportedly been reached.

Italy’s foreign minister held talks in Tehran this week and announced on Wednesday that Rouhani would visit Rome “in the coming weeks”. A memorandum of understanding with Italy’s development ministry and export credit agency was signed.

Top officials from Spain, Austria, Serbia and Switzerland have also recently travelled the road to Iran. Such missions received official EU blessing following a ground-breaking Tehran trip in July by Brussels foreign policy chief, Federica Mogherini.

Europe’s enthusiasm for re-engagement has been welcomed by Iranian government leaders who, like Obama, face domestic opposition from conservative critics of the nuclear deal.

They calculate that the faster and deeper the rapprochement with Europe, the harder it will be to isolate Iran again, even if the nuclear deal collapses. And other major international players like China and Russia, which disliked sanctions all along, will help accelerate Iran’s rehabilitation, if only to steal a march on the US.

“We are recently witnessing the return of European investors to the country,” Mohammad Khazaee, Iran’s UN ambassador, declared with evident pleasure. “Even in the past couple of weeks we have approved more than $2bn of projects in Iran by European companies.”