"Time is of the essence," Rasmussen said as he arrived for a two-day NATO summit in Newport, Wales.
"We need to know very soon whether (the accords) will be signed," he said, adding: "We are approaching the date when that decision has to be taken."
The accords cover the legal status of US and NATO troops who will remain in Afghanistan after the alliance ends its longest ever combat operation there at the end of this year.
The June elections have failed to produce a new president as both candidates claim their opponent rigged the vote despite repeated US efforts to get them to accept the results of an audited recount.
Outgoing President Hamid Karzai decided not to come to the NATO summit, which was supposed to sign-off on the training mission, with Kabul likely to be represented only by its defence minister.