Ambassadors from the remaining 27 member states said residency rights should continue after Brexit as Britain will still be bound by all EU laws during the transition phase.
But Mr Rees-Mogg insisted the cut-off date specified in a joint EU-UK report published in December had to be honoured.
He said: “Free movement must end when we leave on 29th March, 2019. Otherwise we will not have taken back control in the way demanded by the referendum result.”
The 27 envoys were discussing details of a new mandate for the European Commission which is negotiating on the transition period and a new trading relationship with the UK.
The joint EU-UK document gave “the specified date” for EU citizens’ eligibility to secure UK residence as March 29 2019 but left room for “appropriate adaptation”.
And the EU envoys endorsed a note from the Commission which said: “The specified date should be defined not as the date of the United Kingdom’s withdrawal, but as that of the end of the transitional period.”
They also broadly supported the possibility of extending the transition period beyond two years if more time is needed to negotiate a new free trade agreement with Britain.
Diplomats said the EU position on citizens’ rights was less politically controversial now because immigration was no longer red-hot issue it was at the time of the referendum.
One official said: “If anything, today, there’s a big exodus from the UK. Many Poles are leaving. Many British pensioners are leaving for the Spanish sun to become retirees there while they still can.
“If anything, I’d say the UK has a problem with attracting workers today.”