"We need to have this resolution urgently, we need to send this very strong message to the population that is desperate and when you hear now rockets falling into civilian quarters we need a strong voice from New York," Heusgen said on Thursday.
He added, "We want to have this resolution, we want to have a strong resolution and a strong resolution within the united council, everybody is behind it."
According to the special envoy, the political process in Libya has not seen any progress yet and the potential of violence escalation increases with the influx of arms.
On Tuesday, the United Kingdom submitted the draft resolution which calls for an immediate ceasefire and the cessation of hostilities in the North African country.
Libya has been in a critical political situation since April 4, when the Libyan National Army (LNA) commander, Khalifa Haftar, backed by the parliament ruling the country's eastern part, announced an offensive against Tripoli in a bid to drive what he called terrorist forces out of the city. In response, armed forces loyal to the Tripoli-based Government of National Accord (GNA) started a military operation against the LNA.