The formal statement, drafted by Estonia and Norway and seen by Reuters, has to be agreed by consensus by the 15-member body.
The text also "strongly affirms that the Islamic Emirate of Afghanistan is not recognized at the United Nations and declares that it does not and will not support the establishment of any government in Afghanistan imposed through military force or restoration of the Islamic Emirate of Afghanistan."
The UN special envoy for Afghanistan, Deborah Lyons, last week questioned the Taliban's commitment to a political settlement, telling the Security Council the war has entered a "deadlier and more destructive phase."
"The Security Council condemns in the strongest terms possible the armed attacks by Taliban forces on cities and towns across Afghanistan, resulting in high numbers of civilian casualties," the draft statement reads.
The draft text also underlines a council "readiness to impose additional measures on those responsible for violations or abuses of human rights or violations of international humanitarian law, including those involved in attacks targeting civilians, and individuals or entities engaging in, or providing support for, acts that threaten peace, stability or security."
The United Nations said on Thursday it is particularly concerned about a shift in fighting in Afghanistan to urban areas, warning that if a Taliban offensive reaches the capital Kabul it would have a "catastrophic impact on civilians."
The Taliban has stepped up its campaign to defeat the U.S.-backed government since April as foreign forces complete their withdrawal after 20 years. The Islamist militants now control about two-thirds of Afghanistan.
The group claimed control over two of Afghanistan's biggest cities on Thursday, according to media reports, as the United States and Britain said they would send thousands of troops to help evacuate their embassy staff.
The fall of major cities was a sign that Afghans welcome the Taliban, a spokesperson for the group said, adding they would "not close the door to the political track," according to Al Jazeera TV.