The scale of the scam, which police believe is the work of an organized crime gang, has surprised authorities, the BBC reported.
The text message, which began to appear people's cellphones on Monday, reads: "Sum1 paid me to kill you. Get spared, 48hrs to pay $5000. If you inform the police or anybody, death is promised."
It includes a link to a Yahoo email account police have now disabled.
Det. Supt. Brian Hay said some people, mostly those with little experience of text messaging, had fallen for the scam.
"Do not respond," Hay said at a news conference. "Delete it immediately and don't panic ... because that's what they prey upon."
The scale of the scam was "unprecedented," he said.
"We've never seen this anything like this before -- to have so many people contacted at the same time."