He indicated further details of exactly how the UK will manage immigration would be published in due course, but said it would be "wrong to suggest" freedom of movement would continue unchanged.
It comes amid reports of deepening Cabinet splits over post-Brexit immigration, with one group of ministers led by Chancellor Philip Hammond arguing for a system close to the current one and another wanting tougher controls.
Speaking on Monday, Ms May's spokesman said: "Free movement will end in March 2019. We've published proposals on citizens' rights. Last week the Home Secretary said there would be a registration system for EU nationals arriving post-March 2019.
"Other elements of the post-Brexit immigration system will be brought forward in due course.
"It would be wrong to speculate on what these might look like or to suggest that free movement will continue as it is now."
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