BRUSSELS—The leaders of the European Parliament are threatening to veto the bloc's multi-annual budget because of its deep cuts.

The Christian Democratic EPP, the largest group in the legislature, said the 7-year budget worth (EURO)960 billion ($1.28 trillion) must be revised to realistically reflect the EU's growing competences and responsibilities.

Socialist leader Hannes Swoboda called the budget—which needs parliament's approval—unacceptable and said there won't be a majority for the proposed plan.

The EU's 27 member states earlier this month agreed on a budget deal that foresees the first cuts in the bloc's history for the years 2014-2020.

EU President Herman Van Rompuy defended the plan as shifting funds toward growth-friendly investment while recognizing the need to tighten belts currently felt across Europe.