Emily Thornberry has called on the government to guarantee the rights of EU nationals currently living in the UK.
The Shadow Foreign Secretary said foreign nationals worried about their future had been to her surgery "in tears".
The Joint Committee on Human Rights has tabled an amendment to the government's Brexit Bill to protect the residence rights of EU nationals in the UK.
The Bill was given the go-ahead by parliament on Wednesday, after two days of intense debate, by a majority of 384.
Speaking on the BBC's Andrew Marr Show, Ms Thornberry said:
The Prime Minister told MPs on Wednesday it was her "intention and expectation" the government would be able to offer assurances about the position of EU nationals resident in the UK although she wanted see similar assurances for British nationals in the EU.
"We will be working to try to ensure that this is an issue we can deal with at the very early stage in the negotiations," said Theresa May.
"It was one of the objectives I set out in the plan. It will be referenced in the white paper," she added.