President Donald Trump has threatened "much higher" tariffs on the European Union (EU) by 4 July if the bloc fails to drop its levies on the US to zero.

After a phone call with European Commission President Ursula von der Leyen, Trump said the EU had signed a "historic trade deal" with the US and agreed to cut its tariffs.

"I agreed to give her until our Country's 250th Birthday or, unfortunately, their Tariffs would immediately jump to much higher levels," he wrote on social media.

However, von der Leyen said the bloc was making "good progress towards tariff reduction" ahead of Trump's deadline.

"We remain fully committed, on both sides, to its implementation," she said on X.

The trade deal was struck by von der Leyen and Trump in July last year, but progress on enacting it stumbled on Wednesday after talks between EU lawmakers and governments ended without an agreement.

Under the agreement, US tariffs on exports from the EU would face a 15% tariff. Trump had threatened tariffs of 30% on European goods.

The deal received conditional approval from the European Parliament in March, when a majority of lawmakers backed legislation to implement the agreement, but added several safeguards aimed at ensuring the US honoured its side of the pact.

Parliamentarians voted they would only accept zero tariffs on US goods if European goods made with steel and aluminium were excluded from Trump's global 50% tariff on those metal products.

Despite the progress through parliament, the deal also requires endorsement by the 27 member states.

Earlier on Thursday, before Trump's social media statement, the European Parliament's chief negotiator Bernd Lagne said lawmakers and governments were making good progress on the negotiations but added "there is still some way to go".

The negotiators are set to meet for another round of talks on 19 May in Strasbourg.

"We remain more committed than ever to advance and defend Parliament's mandate so as to provide additional guarantees that will benefit citizens and companies in both the EU and the US," Lange said in a statement.

Last week, Trump accused the EU of "not complying with our fully agreed to trade deal" in a post on Truth Social, and said he would increase tariffs on trucks and cars to 25%.

The original agreement on tariffs and trade was reached after the US President finished a round of golf at his luxury resort in Turnberry, Scotland.