Domestic rates in Northern Ireland must be capped at the same level as they are in England, a spokesperson for the Fair Rates Campaign has said.
The government has suggested rates in NI could be capped
Anne Monaghan was speaking after news that a cap on rates under the new capital value system would be part of a package aimed at restoring devolution.
However, Ms Monaghan said campaigners would not accept a cap at £500,000.
Further rates relief for pensioners on lower incomes could also be included in the deal offered by the government.
"It's important to note that the principle of the cap has now been established, but the devil is in the detail," Ms Monaghan said.
"We will not accept a cap at £500,000 because that does not apply anywhere else in the UK.
"The detail is important and we will be looking, now that the principle has been established, for relief for single people and also relief for those above £320,000 - as it is in England."
The first new rates valuations were sent to householders in Northern Ireland at the start of July, and those who wish to challenge or query their rates estimate have six months to do so.
More than 7,000 homeowners have already challenged the rateable estimates of their homes.
The government had previously insisted there would be no cap on bills.
Anyone who wants to check the value of their home can do so by logging onto the Valuation and Lands Agency's website at www.mycapitalvalueni.gov.uk.