According to a European Parliament spokesman, the assembly will elect its president on 3 July even if the European Council fails to decide on other key posts in the bloc.
"There is no way to modify", the decision to hold the vote on 3 July, a spokesman for the European Parliament said.
The MEPs set a deadline for candidates to submit their applications for the Wednesday leadership vote at 20:00 GMT on Tuesday.
In the meantime, the leaders of European governments and states are debating nominations for the heads of the European Commission, European Council, European Central Bank and European Parliament, and the High Representative of the Union for Foreign Affairs and Security Policy.
Commenting on the struggle between the candidates, French President Emmanuel Macron has noted that the deadlock on this issue reflects ongoing "political disagreements between the countries" within the bloc.