Vincent Hannah claimed he was a member of the far-right National Front during the call.
Hannah made the alcohol-fuelled phonecall to the emergency control room at Bilston, Midlothian, at 5:30am on 17 January.
He admitted making grossly offensive phonecalls by uttering threats and using racially offensive language at Edinburgh Sheriff Court on Wednesday, and was fined £400.
The court heard that Hannah, 51, launched the outburst after watching and reading coverage of the Paris terrorist attacks in early January.
Fiscal depute Mark Keane said Hannah phoned 999.
When the call operator asked if he needed help, Hannah repeatedly said: “Get all those Muslims out this country, they have killed our people.”
The operator again asked Hannah if he needed police, and he replied: “No I dinnae – this is the National Front here by the way. The police don’t give a f*** about this country, and you dinnae, because all the Muslims in the country, I’m going to kill them.”
Police traced Hannah’s address at Gowkshill, Gorebridge, from the phone number he had called from and arrested him.
Mr Keane said: “He [told police] he had made a call to 999 that morning. He said that he regretted it; it was very stupid and that he had been drunk at the time. He said he shouldn’t have phoned and said he was drunk and feeling sorry for himself.”
Defence agent Neil Martin told the court that Hannah had got upset after reading about the three-day terror attacks by Islamic extremists in France. Seventeen victims died in the attacks, which included a massacre at the offices of Charlie Hebdo magazine and two sieges.
Mr Martin stressed that Hannah’s comments were “not views that he holds”, reflected by his statement to police in which he said there was “no excuse”.
He said: “That sums up his position. To say he’s ashamed of what he did would be something of an understatement.
“He has been left utterly mortified by his conduct. The day prior to the morning the call was made was the anniversary of his brother passing away.”
He said Hannah, a roadsweeper at Midlothian Council, had been drinking and was on medication. “This was around the days when the terrorist attacks had been carried out in Paris last month,” said Mr Martin.
“He had been watching the news coverage constantly in addition to reading comment on the internet.”
Sheriff Gail Patrick fined Hannah £400, and said: “The emergency services are far too busy to cope with people like you. But I’m encouraged that you don’t hold these views, because terrorists are one thing, and Muslims are quite another.”