Andy Burnham, the mayor of Greater Manchester, has become the latest leader to threaten to stop housing new asylum seekers as the government came under pressure to listen to the concerns of northern communities.

Burnham said there was “mounting chaos” in the government’s dispersal system, which was facing “catastrophic failure”. He said the region’s public services could not continue to support “disproportionate” numbers of people compared with elsewhere in the country. However, in a letter to Yvette Cooper, seen by the Guardian, the Home Office has resolutely stood by its position.

Cooper, the chair of the home affairs select committee, published a scathing critique of the asylum dispersal system earlier this year following an inquiry, and described some of the conditions that refugees were housed in as a “disgrace”. Cooper wrote to the immigration minister, Caroline Nokes, about the issue on 3 October.

In response, the Home Office showed no plans to shift its position and outlined its commitment to the current scheme with the intention to source mainly or only in the private rental market.

Since 2012, accommodation has been provided to asylum seekers via six regional contracts, which are delivered by three providers – Serco, G4S and Clearsprings Ready Homes. The committee report said the poor standard of asylum accommodation was the most significant issue identified in the evidence it received, which focused largely on contracts administered by G4S and Serco.

In the letter, Nokes said: “The Home Office will continue with this work and following the award of the new contracts will ensure that local authorities are engaged in the transition of the services to new providers and that the engagement processes under the new contract operate effectively.”

The government also stated that it had no plans to shift its position on direct funding of the scheme.

Earlier this year, the Guardian reported that the UK’s asylum dispersal system was on the brink of collapse amid growing criticism from political leaders over the way it was being run. Joint letters were written by 14 leaders of councils across Yorkshire, Middlesbrough, Newcastle and Sunderland, the Welsh and Scottish governments.

They warned the government that the voluntary system, which provides accommodation in local authorities for those seeking refugee status, was on the verge of “catastrophic failure”. There were 26,350 asylum applications in 2017.

Burnham has written to the home secretary, Sajid Javid, demanding an urgent meeting and accusing the Home Office of showing “blatant disregard” for the issues the region has been facing.

In his letter, he said the north-west of England hosts 25% of the national population of asylum applicants who require housing and support, 70% of whom are housed in Greater Manchester.

The latest figures show there were 6,681 supported asylum seekers in Greater Manchester – a 102% increase since 2003. The mayor said demand for asylum accommodation had increased by 58% since April 2014.

The dispersal system places high numbers of asylum seekers in some of the country’s poorest communities, largely due to the availability of cheap housing. This means that more than 180 local authorities across the country house no asylum seekers at all – including Theresa May’s local authority of Windsor and Maidenhead.

Describing Greater Manchester’s compliance with the system as “voluntary”, Burnham wrote: “It cannot be right that towns in Greater Manchester have more asylum seekers clustered in a handful of wards than entire regions in the rest of the country.”

A Home Office spokesman said it would respond to the letter “in due course” and added: “We take the wellbeing of asylum seekers and the local communities in which they live extremely seriously.”

Later this month Nokes was due to meet council leaders from Yorkshire and the Humber after they also warned that they were considering pulling out of the scheme. The region hosts around 5,000 asylum seekers. Northern councils have said they were being increasingly sidelined.

The decision to write en masse to the government has been prompted by the new asylum accommodation contracts – one of the government’s largest procurements, worth more than £4bn over 10 years – which have been put out to tender. They would replace the existing Compass contracts, delivered by G4S, Serco and Clearsprings in 2019.

Local authorities fear they may have to accept higher numbers of asylum seekers and poorer-quality accommodation so the government could persuade a company to run the scheme.

Sir Steve Houghton, the leader of Barnsley council, told the Yorkshire Post: “We hope the home secretary will pause and listen to these real concerns of local areas in the north. The clock’s ticking down, but we remain hopeful that in the next two weeks the government will commit to a fairer distribution of asylum seekers around the country, proper partnerships between national and local government and funding for us to support people placed in our local communities.”

Sabir Zazai, chief executive of the Scottish Refugee Council, said: “This current approach of ignoring communities’ concerns is not sustainable and it’s not fair.

“We can’t understand why the Home Office would choose to ignore this expertise that’s been built up on the ground over so many years, but by rejecting calls from councils for direct funding and oversight powers, that is what they are doing. What really worries us is the impact this will have on people in need of refugee protection.”