Key issues over the resettlement of 20,000 Syrian refugees to the UK still need to be "urgently resolved", the Local Government Association says.
It comes after the first refugees admitted to the UK since the government announced it was expanding its protection scheme arrived on Tuesday.
The LGA warned councils still did not know how the scheme would work, nor what financial support they would get.
However, the Home Office said it was working closely with local authorities.
Earlier this month, Prime Minister David Cameron pledged to take 20,000 Syrians living in camps bordering Syria by 2020.
Mr Cameron said the scheme would be funded for the first 12 months by the government.
The LGA - which represents more than 370 local authorities in England and Wales - urged clarity on details, including how the scheme would be funded.
"We are pressing the government on exactly how the scheme will operate," said David Simmonds, chairman of the LGA's refugee task group.
"We need to know who is arriving and when in order to ensure that we have the right homes, school places, and other support that may be required.
"There are a number of issues that need to be urgently resolved, in particular the need for a firm commitment that councils resettling refugees will receive full financial support, in order that it is not seen later as an unfair burden on communities that open their doors."
The Home Office insisted detailed information about individual refugees had been shared and it was working closely with the UN refugee agency and local authorities.
What happens when refugees arrive?
Dominic Casciani, BBC News home affairs correspondent
Once someone has been identified and approved, they have full legal rights to settle in the UK for five years - and for the first months, they will be accompanied every step of the way into their new life.
When they arrive in the UK, they are met at the airport by a welcome team who take them to their new home. And the next morning, their personalised integration plan begins.
Just like anyone else, they can work and claim benefits. Everything about life in the UK is explained to them in briefings and classes.
School places are ready for their children, there is a GP already set up to take them on and, where necessary, specialists to work on their long-term health problems.
There are trips to the job centre and colleges for those ready to go back to work or study.
Under the VPR scheme, the refugees will be granted five years' humanitarian protection, which includes access to public funds and the labour market, as well as the possibility of family reunion, if a person was split up from their partner or child when leaving their country.
After that period they can apply to settle in the UK.
Eventually the UK will have to take about 400 refugees a month in order to meet its 20,000 target by 2020.
Those being resettled will come from camps in countries neighbouring Syria and will be selected by the UN on the basis of need.
Britain has been under pressure to take in more people as Europe struggles to deal with a huge influx of refugees.
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