Debenhams has written to the Welsh Government asking it to take urgent action to save four of its stores and “many hundreds of jobs”.
The retail giant collapsed into administration for the second time in a year in April after coronavirus ramped up the pressures facing the business.
Deals with landlords mean 120 UK stores will reopen when lockdown eases.
The firm wants Welsh ministers to review rates. Officials said they would respond to the request “in due course”.
Debenhams has continued to trade online since entering administration again on 9 April.
It then used another insolvency process called a company voluntary arrangement to obtain rent cuts and allow it to close shops.
The company warned at the end of April that four of its Welsh stores – Newport, Cardiff, Swansea and Llandudno – were in jeopardy because of the Welsh Government’s decision not to extend business rate relief to properties with a rateable value of more than £500,000.
Since then, Debenhams has struck deals with local councils to defer payment of the rates for those stores until March 2021.
These stores are due to reopen when the Welsh Government lifts restrictions on non-essential retailers, but the long-term future remains uncertain.
Last week the chairman of Debenhams’ parent company, Mark Gifford, wrote to the Welsh Government’s Finance Minister Rebecca Evans asking her to give permission for an online tribunal to review the business rates.
“With your support for holding tribunals online, the administrators would be in a position to reopen all the remaining Welsh stores, saving many hundreds of jobs in Wales,” he said.
“We urge the Welsh Government to consider this as a matter of urgency, we are ready to reopen all of our Welsh stores when trading restrictions are lifted.”
As well at these four at-risk stores, Debenhams also has shops in Carmarthen, Llanelli, Merthyr Tydfil, Bangor and Wrexham.
Mr Gifford said because Debenhams has negotiated changes to its lease arrangements, the tribunal review would result in a significant reduction in business rates and lead to earlier payments of those rates to Welsh Government.
The letter said such tribunals cannot be held at the moment because of social distancing concerns “or unless the Welsh Government steps in and agrees that tribunals could be held online”.
A Welsh Government official said: “While we know how important Debenhams stores are to our town centres, this is a business facing its third insolvency process in 12 months.
“It is simply not credible to suggest our decisions about rate relief will cause Debenhams to fail.
“Taxpayers are already providing more than £1m in rates relief support to Debenhams across Wales.”