Joseph Daul, chairman of the centre-right European People's Party (EPP), Martin Schulz, chairman of the Socialists & Democrats group, and Guy Verhofstadt, chairman of the liberal ALDE group, said the European Union was in danger of "moving backwards" in attempting to make its voice heard on the world stage.
The proposal currently on the table "represents the outcome of preparatory work undertaken by the Council and the permanent representatives of the member states," the three lawmakers write in a joint statement.
"It does not reflect the Community interest or promote a genuine European added value, but rather the return of intergovernmentalism," they warn.
The European Parliament is not directly involved in setting up the EEAS, but its approval will be needed to pass the new institution's budget, making it an important player in the negotiations.
"Today we need a 21st century approach which should be embodied by the new External Action Service," argue the leaders of the Parliament's three largest political groups.
"During the 19th and 20thcentury, foreign policy was organised in a vertical and exclusive way - separating out all the components of external action. We should leave that model behind," they continue.
From the outset, Parliament has supported making the EEAS a full part of the European Commission in terms of its administration and budget. It also argued in favour of bringing together current Commission and Council services dealing with crisis resolution, development and other policies.
By contrast, the proposal put forward in March by Catherine Ashton, the EU's foreign policy chief, foresees a loose coordination and consultation between the Commission and Council services, as well as other EU bodies.
The Council represents the interests of EU member states and can be compared to the US Senate in terms of its position in the EU institutional set-up.
EU foreign affairs ministers will meet on 26 April in Luxembourg and are expected to discuss a re-vamped proposal from Ashton. The Parliament had rejected her early draft in March (see 'Background'). To prepare for the meeting, the proposal will also be discussed at ambassador level.
According to AFP, Ashton has shelved the idea of an over-arching secretary-general, opting for a more horizontal system with three more or less equal deputies, although their responsibilities remain unclear.
What is certain is that bigger countries are putting forward their candidates, with Pierre Vimont, French ambassador to the United States, seen as a front runner.
In the tight schedule ahead, it remains unclear what room is left, if any, for consultations with Parliament.
"Unless and until the Council and the Commission are prepared to initiate real negotiations with the Parliament, no progress can be made on this important issue. And to achieve this, Parliament is prepared to fully use its powers of co-decision," the leaders of the three groups warn.
