Linfield say they are 'bemused' at the decision to move their big two clash with Glentoran from Easter Tuesday to accommodate the arrival of US President Joe Biden.
Th Belfast club said, in the interests of fairness, other scheduled games should be changed.
Police said they have asked for the other Belfast games to be rescheduled as well.
The Linfield game, which was due to take place on April 11 at Windsor Park, has been delayed the Northern Ireland Football League (NIFL) until Wednesday, April 12.
However, two other games in north Belfast, less than three miles from Windsor Park, are to go ahead, which could have a potential impact on the title race.
In a statement Linfield said it has concerns at the impact the short-notice change will have on supporters.
President Biden is due to arrive in Northern Ireland on Tuesday 11 April, and a high security presence is expected during his visit in Belfast meaning police resources will be stretched.
The chief constable has already said officers will be drafted in from other parts of the UK to support the PSNI for the visit.
Cliftonville's game against Larne at Solitude and Crusaders vs Coleraine at Seaview are unaffected, despite taking place on the same day. In a statement Linfield said it received correspondence from NIFL on Wednesday evening suggesting its home fixture against Glentoran would be moved from Easter Tuesday, "due to a PSNI decision relating to operational pressures, as a result of the upcoming US Presidential visit".
"While we accept that this decision may be necessary, given policing levels, we have concerns at the impact this short notice change will have on our supporters," the club said.
"Furthermore, we were bemused that two other NIFL fixtures have been given permission to go ahead in North Belfast, under three miles from Windsor Park.
"Given that there are only five league games left, in the interests of fairness and sporting integrity, we suggested to NIFL that all Easter Tuesday games, be moved to Tuesday 18 April, as there is currently a scheduled game for TV involving one of the impacted clubs on Friday 14 April.
"This would ensure no team would be afforded a sporting advantage, or suffer a sporting disadvantage.
"We outlined our position to NIFL and expressed a strong desire to engage in face-to-face meetings with both the PSNI and NIFL. We have not been afforded that opportunity.
"This is an extremely disappointing outcome which impacts on our loyal supporters who have bought tickets for this game in good faith and made arrangements accordingly during the busy Easter period."
The PSNI said following discussions with NIFL they requested that all three Belfast matches on Easter Tuesday be rescheduled.
Chief Superintendent Darrin Jones added: “I have made this request as we anticipate an unprecedented high demand for policing resources across the organisation, particularly in the Belfast area on Easter Tuesday, 11 April.
“Unfortunately, the scheduling of three games together at Solitude, Seaview and the National Stadium would require a significant level of policing support.
“I have made this request based on current risk assessment and the policing footprint required to ensure public safety and prevent disorder.
"I apologise to the Northern Ireland Football League, the clubs and fans for any inconvenience this may cause, but hope everyone understands and agrees that public safety at these large events comes first.”
The Northern Ireland Football League said: "The NIFL Competitions Committee considered the request from Linfield for all fixtures on Tuesday 11 April to be moved.
"This request was declined with the re-schedule viewed as being consistent with fixture scheduling throughout the season."
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