Ministers will seek to overturn the defeat in the House of Lords on the Government's Brexit Bill when the legislation returns to the Commons, Government sources said.
Peers defied Theresa May, voting by 358 to 256 in favour of an opposition amendment guaranteeing the rights of EU nationals living in the UK after Brexit.
The Government described the first defeat to be inflicted on the Bill during its passage through Parliament as "disappointing" but made clear they were determined to reverse it in the lower chamber.
A spokesman for the Brexit Department said: "The Bill has a straightforward purpose - to enact the referendum result and allow the Government to get on with the negotiations.
"Our position on EU nationals has repeatedly been made clear. We want to guarantee the rights of EU citizens who are already living in Britain, and the rights of British nationals living in other member states, as early as we can."