Tom Evans, 21, and Katie James, 20, said sorry after a protest outside Alder Hey Children's Hospital allegedly intimidated doctors and nurses and threatened to cut short their precious last moments with the 23-month-old tot.
Mr Evans begged in an earlier Facebook post: "Can I ask that after tonight I would really appreciate if everyone has a break from the protesting please?"
"Me and Kate need to now focus on spending precious time with Alfie and focus on the next legal step, keeping the relationship with the staff at ease and peace and make sure no parents are being affected any more".
One patient's relative, who did not want to be named, told BBC Radio Merseyside that visiting Alder Hey was "intimidating and scary" and that she heard chants of "burn it down" from protesters, which she said was "taking it too far".
Chief Inspector Chris Gibson said officers "recognise the sensitivities involved in this very hard and sad situation".
'This is extremely unhelpful for all concerned and we are investigating further to establish the full circumstances.
"We would like to remind the public that this is a hospital for sick children and it should not be forgotten that many families are going through extremely challenging and emotional times". While hospital doctors say the baby is essentially braindead and has no quality of life, parents Tom and Kate have video footage showing the baby yawning, stretching, and responding to various stimuli.
Appeal court officials said an appeal court judge had decided that Alfie should continue to receive treatment pending the outcome of the hearing that begins on Monday.
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It is thought that Supreme Court justices may now be asked to consider the case.
Wiping away tears and visibly shaking, he thanked supporters surrounding him and again asked for his son's life not to be terminated and for other doctors to be allowed to "look after him".
However, Alfie's parents are determined to keep fighting.
Alfie Evans, who is 23-months-old, has been battling chronic seizures since 2016 as a result of an undiagnosed degenerative brain disease.
Justice Moylan also said that the baby's independent guardian has agreed with the hospital that withdrawing ventilation is in the baby's "best interests".
In statement Alder Hey said it "refuted" criticisms from Mr Evans of the treatment Alfie has received.