Prison officer Adrian Ismay died days after car bombing in Belfast in March.
DUP MP Gavin Robinson alleged in the Commons that a police email said checks were resulting in "too many complaints" from the suspect's solicitor.
The Police Service of Northern Ireland said they "rigorously enforce all bail conditions set down by the courts".
"If a person is required to wear an electronic tag as part of their bail conditions, there is no reason for police to duplicate this monitoring unless otherwise requested or directed by the investigating officer or senior police officer or the court," a PSNI statement said.
The bail checks refer to Christopher Alphonsos Robinson who has been charged with the murder of Mr Ismay, who trained prison officers at Maghaberry Prison.
Dissident republicans claimed responsibility for the attack.
The accused, from Aspen Park in Dunmurry, west Belfast, was granted bail under strict conditions in May.
The conditions including electronic tagging and an exclusion order for an area of east Belfast.
Speaking during a Westminster debate, the DUP MP said: "I received information at the weekend that PSNI chiefs sent an email to their officers not to conduct bail checks because it was generating far too many complaints from his solicitor and offending his sensitivities."
In response, a PSNI statement said: "Police will continue to rigorously, but impartially, enforce all bail conditions set by the courts and we will not hesitate to arrest those who breach their bail conditions."
The House of Commons debate focused on Libyan-sponsored terrorism.
The MP said Mr Ismay "was blown up by a bomb planted by the new IRA containing Semtex, which is presumed - since there have been no recent purchases - that it is of the same origin and extraction, sourced from the Czech Republic, through Libya to the IRA and disseminated through their splinter organisations."
Police officers have been asked to stop conducting bail checks on a man accused of murdering a prison officer, the MP for East Belfast has claimed.