The US remains fully committed to supporting Afghanistan despite a plan to pull out thousands of troops, the visiting defence secretary has said.
Rumsfeld says the US is committed to a long-term relationship
Donald Rumsfeld was speaking after meeting Afghan President Hamid Karzai in the capital Kabul.
On Tuesday Mr Rumsfeld said the US would pull out between 2,000 and 3,000 of its 19,000 soldiers in Afghanistan.
Afghan officials had expressed concerned that any troop withdrawal by the US would embolden militants.
"We certainly remain committed to our long-term relationship," Mr Rumsfeld said at a joint press conference with President Karzai.
Mr Karzai added: "The United States has assured us of continued support and assistance on all matters."
The BBC's Andrew North in Kabul says the plan is that soldiers from other Nato states will take the place of the withdrawing Americans as Nato expands operations into more areas of the country.
The US will reduce its troop numbers by 2,000 to 3,000
But he says there is still uncertainty over how quickly other Nato countries will fulfil their commitment.
There is concern that militants may be deliberately focusing attacks on non-American troops in an attempt to undermine support in their home countries for further deployments.
The most recent attack was on Italian peacekeepers in western Afghanistan.
Canadian troops currently serving in the south under US command, but who will make up one of the key components of the Nato force there in the New Year, have been hit by suicide bombers three times in recent weeks.
A high-ranking Afghan government official, who did not want to be named, told the BBC that any reduction in the number of US troops would affect morale in the country.
"This will help the Taleban and will have a negative impact on security," the official said.
But Mr Rumsfeld has insisted the troop reduction will not weaken US operations, mainly in the south and east, against militants linked to the Taleban and al-Qaeda.
"We are probably going to be able to draw down about 2,000 or 3,000 US troops," Mr Rumsfeld said.
"We will still have more total US troops in Afghanistan than all of the [other Nato] nations combined," he said.
"The country has now gone through a presidential election and parliamentary and provincial elections and we were able to make those [army] adjustments," Mr Rumsfeld said.