A slightly watered-down version was put forward by Britain on Wednesday but the three African countries on the council – Equatorial Guinea, Ivory Coast, South Africa – blocked it.
Russia also said the proposed measure even after it was amended was "still far away from accommodating our concerns," according to a note from the Russian mission seen by AFP.
Haftar, seen by his allies Egypt and the United Arab Emirates as a bulwark against Islamists, has declared he wants to seize the capital, now controlled by a UN-recognised government and an array of militias.
Haftar backs a rival administration based in eastern Libya that is refusing to recognise the authority of the Tripoli government.
The revised text did not single out Haftar's forces, but instead expressed "grave concern at military activity" near Tripoli, "including the launching of a military offensive by the LNA," Haftar's self-styled Libyan National Army.
The three African countries insisted that there be a reference to an African Union statement on the need for all parties fighting in Tripoli to protect civilians including migrants and refugees, according to documents seen by AFP.
US DRAGGING FEET
Britain had hoped to hold a vote before Friday, but that now appeared unlikely.
Diplomats said the United States appeared to be dragging its feet in pushing for a quick adoption of the draft resolution.
The proposed measure would echo a call for a ceasefire by UN Secretary-General Antonio Guterres, who was in Libya to personally advance prospects for a political solution when the offensive was launched.
Haftar's offensive forced the United Nations to postpone a national conference that was to draw up a roadmap to elections, meant to turn the page on years of chaos since the 2011 ouster of Muammar Gaddafi.