Many foreign workers have been returning home
Ministers have been warned that making it tougher for migrants to become citizens may slow an economic recovery.
New rules governing how migrants must "earn" citizenship could deter workers needed to fill vacancies, says the Institute for Public Policy Research.
The warning came as ministers prepare to introduce legislation on immigration and border security into the Commons.
They say it will make immigration procedures more effective but opponents say it will be costly and inefficient.
Proposals contained in the Borders and Immigration Bill, to be published on Thursday, include making migrants who refuse to integrate or commit crimes wait longer to obtain citizenship.
But the left-leaning Institute for Public Policy Research (IPPR) said such restrictions might create uncertainty at a time when the UK economy desperately needed skilled workers.
"Migrants become easy targets at times of economic difficulty but introducing yet more tough measures to exclude people could damage our prospects for economic recovery," said the body's head of migration research, Tim Finch.
Greater clarity was needed about what migrants must do in terms of contribution to British life to earn the right to citizenship, he said.
Concerns about migrants' access to benefits and housing while on so-called "citizenship probation" must also be addressed in a fair and open manner, the IPPR says.
"Not all migrants will want to settle in the UK but some will and so it is important that the over-complicated process of earned citizenship is made more clear and fair," Mr Finch added.
The IPPR said there was already clear evidence that the downturn was depressing immigration levels and this trend was likely to continue.
There was a real risk that vacancies in areas such as construction, teaching and social care, which may not be filled by British workers, would go unfilled if tougher curbs on immigration were introduced, it claimed.
Ministers argue that the new proposals, on top of the points-based migration scheme for non-EU nationals introduced last year, will simplify and improve immigration procedures.
But opposition parties say the government has still failed to reassure the public it has immigration levels under control.
The Conservatives say the new citizenship process is likely to be cumbersome and bureaucratic.
The Lib Dems argue the new proposals are an admission of past failures to control British borders.