Mr Eide will tell member nations that the international community needs to 'demilitarize' its overall approach in Afghanistan if it is to reverse current trends.
"We have to get into a mode where our strategy is politically driven and not militarily driven, where the political and civilian components become an appendix to a military strategy," Mr Eide told reporters hours before leaving for New York on Sunday.
The UN Envoy also stressed that one of the main objectives of the military troops that will arrive this year is to build the capacity of Afghan Forces.
"I am deeply sceptical (of) a situation where we have an increase of military forces and that increase of military forces engages in political, civilian and humanitarian issues. I say this because...when you have an increased number of troops coming in, there will always be a trend for those forces to demonstrate quick results and take upon themselves political tasks. That leads to quick impact. (But) quick impact very often becomes quick collapse," he added.
The Special Representative will also tell the Security Council on the need to reinvigorate peace talks between the Government and insurgent groups.
This is last time Mr Eide will be addressing the Security Council in his capacity as Special Representative of the Secretary-General for Afghanistan.
Meantime, Secretary-General Ban Ki-moon released his latest report on Afghanistan on Tuesday, where he demanded more international action to reverse the current worsening trends in the country.
The Secretary-General stated there were no indications of early improvement in the security situation in Afghanistan, adding that a better coordinated international effort was crucial to reversing overall negative trends.
Mr Ban also called on the Government and the international community to make the most of the coming months to focus on agreed priorities, with a reinforced international coordination structure under a UN umbrella that will meet the principal needs of delivering services to the Afghan people.
Opportunities for greater engagement between President Karzai and the international community will arise at the conference on Afghanistan that will take place on 28 January in London.
By Aditya Mehta, UNAMA