"All measures must be taken to ensure irregular migrants' effective return, including use of detention as a legitimate measure of last resort," the text said. The EU would create multinational teams to process and deport people when governments were unable to do the job.
African and Asian countries that refused to accept people could lose out on trade deals, aid and other engagements with Europe under a "fine balance of incentives and pressure". Visa arrangements could be cancelled for states refusing to co-operate.
Just four in 10 migrants deemed to have no right to refuge in Europe are deported, figures showed.
May said the EU needed to "up its game" and "break the link" between migrants reaching Europe and being able to stay. "The UK has always argued we should be sending economic migrants back to their countries of origin. It's why we need to crack down on those who are abusing our asylum system."
The interior ministers committed to consider creating regional centres outside Europe. The proposals also suggest prioritising action against migrants with a criminal record, and greater use of biometric data to identify people for deportation.
Today the first planeload of people to take part in the EU's relocation scheme leaves from Rome for Sweden.