The parties will meet on Wednesday evening in the hope of finding a compromise that both sides can accept.
Parliament wants to stipulate that the agreement will only come into force if and when the US has done its part, and that it will expire in March 2028. The issue is dividing the member states, with several strongly skeptical about altering the agreement.
Fresh threats from President Donald Trump to further increase tariffs on cars from the EU have not made the situation any easier.
"The lesson learned... is that a deal today is not necessarily a deal tomorrow. And therein lies the difficulty," Belgian Foreign Minister Maxime Prévot told the news site Politico Europe.
