Businesses and trade unions have called on Theresa May to guarantee immediately the right of EU citizens to stay in the UK after Brexit.
The British Chambers of Commerce (BCC), which represents companies with a combined workforce of five million people, and the TUC made the call in an open letter to the prime minister.
Failure to do so would damage the UK economy, the two bodies said.
Downing Street said Mrs May wanted to protect the status of EU nationals.
The bluntly-worded letter was jointly signed by TUC general secretary Frances O'Grady and BCC director-general Adam Marshall.
"We call upon you to demonstrate leadership by providing EU citizens in the UK with the reassurance we would expect to be shown to UK citizens across the Continent - not by making one conditional upon the other," they wrote.
"Now is the time to end insecurity for EU workers and for British businesses alike."
There were 2.1 million people from EU member nations working in the UK as of March this year, according to the ONS. That was 224,000 more than the total for the first three months of 2015.
Mr Marshall said the government could give an early Christmas present to both businesses and workers by making an "unequivocal commitment" to EU citizens working in the UK.
"Business communities across the UK are deeply frustrated that ministers have declined to guarantee the residence rights of their EU employees and colleagues. Some firms are already losing key members of staff due to this avoidable uncertainty," he said.
"Such a move before the start of a complex Brexit negotiation would be bold, but it is the right thing to do."
Ms O'Grady said: "Continued doubt about the status of workers from the rest of the EU is bad for business, and it puts services like the NHS at risk."
The joint call echoed one made by the TUC and the CBI, which represents businesses employing about seven million workers, the week after voters backed taking Britain out of the European Union.
The two bodies said that the government needed to allay the concerns of EU nationals working in the UK, as well as UK citizens in the EU, as a "matter of urgency".
Last week peers said the UK had a "moral" duty to guarantee the status of EU nationals living in Britain before Brexit negotiations begin.
The Lords EU Justice sub-committee called for an immediate "unilateral undertaking" that EU nationals could continue to live, work and study in the UK after Brexit.
A Downing Street spokesman said: "The prime minister has been clear that she wants to protect the status of EU nationals already living here, and the only circumstances in which that wouldn't be possible is if British citizens' rights in European member states were not protected in return."