"We understand that a deal is a deal," Greer told reporters on the sidelines of an OECD ministerial meeting in Paris on Thursday.
The US has struck deals with the EU and Japan that limit US tariffs on most EU or Japanese imports to a maximum of 15 per cent.
However, Greer's office on Tuesday unveiled a new set of tariffs on 60 countries after determining that they had failed to curb trade in goods made with forced labour.
The EU would face a 10 per cent tariff and Japan 12.5 per cent.
A further Section 301 investigation into excess manufacturing capacity could push overall tariffs on the two economies' goods well past 15 per cent.
Greer, talking about the EU trade deal, said the agreement acknowledged that the United States could impose tariffs "up to a certain level" and that the Section 301 investigations gave US President Donald Trump the authority to do so.
EU Trade Commissioner Maros Sefcovic, who spoke with Greer at the OECD meeting, said both sides agreed "the deal is the deal", which meant for the European side the terms agreed at Turnberry with an all-inclusive 15 per cent tariff.
Sefcovic said EU countries had been surprised to find themselves targeted by tariffs over forced labour on account of their high labour standards.
He expected the EU parliament to approve the Turnberry deal with Trump's administration.
The EU is working to introduce a ban in December 2027 across the bloc on all products involving forced labour, irrespective of whether they originate in the EU or in a third country, Sefcovic said.
