Natalie McNally's parents: PSNI say budget cuts will not impact murder hunt
Noel McNally also made a direct appeal to his daughter's killer to hand himself in to police, stating that women in Lurgan are "scared stiff" while he remains at large.
Ms McNally, 32, was 15-weeks pregnant when she was stabbed in her home at Silverwood Green in the Co Armagh town on December 18.
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Hide AdMore than 1,000 people gathered at a rally in her memory Lurgan Park on Saturday.
It came just days after PSNI chief constable Simon Byrne said budget cuts would mean the force would shrink to its smallest ever level.
He also warned that some services provided by police would inevitably be impacted and there would be fewer officers, fewer vehicles, postponed building maintenance and a potential delayed response to calls.
Noel McNally said the police had told him their investigation would not be affected.
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Hide AdReferring to the fact that nobody has been charged over his daughter's death, he told the PA news agency: "It is very frustrating, but we know the police are putting every effort into catching this person.
"They are really putting everything into it.
"They have even told us that with the financial restraints on the PSNI will not affect this at all, they are going to throw everything they have at it."
"We have every confidence that they will catch this fellow."
Bernie McNally appealed to anyone with information about Natalie's death to contact police.
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Hide AdShe said: "Hopefully people will think and examine their conscience, think if they know anything or are hiding this person.
"Please think, do you really want to be hiding a monster, because that's what he is."
Mr McNally added: "Even that fellow, if he is watching this, give yourself up to the police.
"The whole town (Lurgan) is scared, all the wee girls are scared stiff while you are still out there.
"Give yourself up to the police, do the right thing. You have to do this."