The workers are currently upgrading and installing new electricity meters in the Twinbrook area.
However, the men, claiming to be from the ONH, told the NIE workers they would be shot if they continued installing the new meters.
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Sinn Féin Councillor for the Collin area, Stephen Magennis, condemned the threats and said it is "completely unacceptable".
Mr Magennis said: "No workers should be under such threats. They are working to improve services for our communities and for some unknown reason a group, which has no support in the area, thinks they can issue death threats.
"Understandably the work has stopped due to these threats as employee safety is paramount. Those behind the threat need to withdraw them immediately and explain their rationale to this community. While the threat remains local people will lose out."
(CD)
