A May 1 letter from two of President Donald Trump's top defence officials, seen by AFP, is the latest sign of deep misgivings in Washington about the EU's push to make its military spending more coherent.

The letter to EU diplomatic and security chief Federica Mogherini says "poison pills" embedded in proposed rules would shut third countries such as the US out of European projects -- and hints at retaliatory measures.

The concerns focus on the European Defence Fund (EDF), a seven-year 13-billion euro ($14.6 billion) pot approved by the European Parliament last month, and the EU defence cooperation pact known as PESCO.

"The draft EDF regulation and PESCO general conditions represent a dramatic reversal of the last three decades of increased integration of the transatlantic defence sector," the letter says.

The proposed rules "would not only damage the constructive NATO-EU relationship we have built together over the past several years but could potentially turn the clock back to the sometimes divisive discussions about EU defence initiatives that dominated our exchanges 15 years ago," the letter warns.

Along with the warnings, the US officials also make a veiled threat to hit back, saying the EU would object to similar US restrictions "and we would not relish having to consider them in the future".

EU countries launched PESCO in late 2017 to try to harmonise a highly fragmented approach to defence spending.

Under the pact, countries cooperate on projects to develop new military equipment such as fighter planes and drones, and on support systems such as military hospitals and training centres.

The US letter chimes with bitter divisions within the bloc on what rules to set for non-EU allies such as the US, Norway -- and for Britain after Brexit -- who want to contribute to projects.

A group led by France wants to set tough rules, arguing the aim is to improve cooperation within Europe and achieve "strategic autonomy" -- ending the historic reliance on the US to guarantee the continent's security.

A rival grouping led by the Netherlands and Sweden favours a more inclusive approach, arguing that Europe should not shut out longstanding allies with strong defence expertise, like the US.

Washington argues that shutting out third countries by making the rules too tough will ultimately lead to more money being wasted and make it harder to ensure European and US military systems can operate together in NATO.

- Double lock -

European defence officials say there is some misunderstanding of their plans in Washington, insisting that close cooperation with NATO is in place to ensure projects dovetail with the alliance's priorities.

They also note that the money available under the EDF -- 13 billion euros over seven years -- is little more than loose change in the defence sector.

But there is also sympathy in some quarters for US concerns about PESCO.

A government official from one EU state said PESCO should not have "a complete open door" but warned against closing it too far.

"There's a difference with some other countries in the union or within PESCO like France or Spain, who really want to put ten locks on this door and prevent everybody from coming in," the official said.

"At my house I have only two locks and that's enough to keep burglars out but it helps me open it easily and host visitors."

Mogherini said the EU was preparing a "clear and complete reply" to the US concerns, but insisted the EU would remain open to American defence manufacturers.

"The EU is actually at the moment much more open than the US procurement market is for the European Union companies and equipment," she told reporters.

"In the EU there is no 'buy European' act and around 81 percent of international contracts go to the US firms in Europe today."