The Digital Services Act, announced by the European Commission in December last year, requires the tech giants to do more to tackle illegal content such as hate speech and child sexual abuse material.
They will also have to do better against misuse of their platforms that impinges on fundamental rights, and intentional manipulation of platforms, such as using bots to influence elections and public health.
It all centred on an awkward moment at the start of talks between von der Leyen, European Council President Charles Michel and Turkish leader Recep Tayyip Erdogan in Ankara on Tuesday.
The groups also took issue with the power given to national authorities rather than courts to order terrorist content to be taken down across the bloc, saying this amounted to state over-reach.
The accord is designed to permit material of an educational, journalistic or artistic nature or facilitating research designed to raise awareness of the danger terrorism poses.