The DUP has called for new UK government guidance on flying the Union flag to be extended to Northern Ireland.
The flag is to be flown on government buildings in Great Britain every day under new the guidelines from the Department for Digital, Culture, Media and Sport (DCMS).
At present, it is flown on around 20 designated days in England, Scotland and Wales, but from the summer it can be flown all the time.
However, in Northern Ireland the flag will continue to be flown only on designated days.
Flags and emblems remain contentious in Northern Ireland's divided communities.
In 2012 a decision by Belfast City Council to reduce the number of days on which the Union flag is flown from City Hall sparked widespread protests and disorder.
DUP MP Jeffrey Donaldson said it is "bizarre" the UK government is "only deciding in 2021 to fly the Union flag, the flag of our nation, on all government buildings every day".
"When I visit other nations around the world, flying the national flag on government buildings is commonplace," he said.
"The decision to exclude Northern Ireland at this stage is wrong and runs contrary to 'New Decade, New Approach' which sought to align us with the rest of the UK when it came to the Union flag being flown on government buildings.
"This is a matter we will be pressing the government to address."
Northern Ireland is the only part of the UK where designated days for flag-flying are enshrined in law.
In the 'New Decade, New Approach' deal which restored devolution last year, the UK government agreed to increase Northern Ireland's designated dates by three to bring them into line with Britain.
It said this would mean the "same designated days will be observed in Northern Ireland as in the rest of the UK going forward".
Alliance deputy leader Stephen Farry said it was appropriate for Northern Ireland to have different regulations given the divisions over flags.
"You have to of course recognise that Northern Ireland is a divided society and people do have different views on this issue, so it is something to be approached with a degree of sensitivity," he told BBC Radio Ulster.
"It's important to also recognise that the law in Northern Ireland is set out through secondary legislation, so this is guidance for the rest of the UK. Northern Ireland is under a different regime and that is appropriate.
"More broadly, I am somewhat depressed that we are back discussing the flying of flags and that there are many other important issues going on in our society and we need to address."
Meanwhile, the UK government on Wednesday night published a long-awaited review on strengthening the Union.
Among the recommendations are a dedicated cabinet post, a fund for UK-wide projects "to incentivise" cooperation between the four nations, and placing UK government branding on projects it funds in the devolved regions.
The Dunlop Review was set up in 2019 by then-Prime Minister Theresa May and was completed in November that year.
Cabinet Office Minister Michael Gove said the UK government shared the review's ambition to "strengthen the ties that bind us across the whole United Kingdom".
Mr Farry, MP for North Down, said he felt "sceptical leaning towards being cynical" about the review.
He said: "English nationalism seems to be dictating the decisions of the UK government and in particular you can't ignore the issue of Brexit and in particular both Scotland and Northern Ireland have very divergent views from the rest of the UK in that regard.
"Simply moving around civil servants, symbolic use of flags, doesn't really cut it."
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