The Parliament's Social Democrats and Liberals initially said no to the proposal that the Swedish member Jörgen Warborn (The Moderate Party) had put forward, but gave in after he opened up to instead make a deal with the far right.
Agreement ahead of Monday's vote was reached after the issue was raised to the group leader level in the Parliament and pressure also came from Spain's Social Democratic Prime Minister Pedro Sánchez, reports the news site Politico Europe.
The S-group's negotiator in the matter, the Dutch Lara Wolters, is however quitting her assignment in protest.
CSR and CSDD deal with, among other things, how companies should ensure that subcontractors outside the EU do not contribute to, for example, environmental destruction and child labor.