Over the next three days they will meet President Karzai and Government leaders, as well as civil society and other representatives.
Included on their agenda are meetings relating to security, governance, human rights, and economic and social development.
They will also discuss how to implement about $20 billion pledged from a donors' conference this year.
A statement from the UN Assistance Mission in Afghanistan -UNAMA says an additional aim of the Security Council delegation is to underline the role of the United Nations in promoting peace and stability.
Since 2002, the UNAMA has been tasked with leading the civilian efforts of the international community.
This is Donn Bobb reporting for United Nations Radio.
(duration: 50")