Updated

NATO Secretary-General Anders Fogh Rasmussen said Sunday that western allies will "stay the course" in Afghanistan despite the death of Usama bin Laden, pushing back on suggestions that the elimination of the Al Qaeda leader should herald the end of the decade-long war.

Rasmussen, in an interview with Fox News, echoed the White House in saying that while bin Laden's death is a milestone, "international terrorism still poses a threat toward our countries."

He said the transition to Afghan responsibility is still set to start this year and hopefully be completed by the end of 2014.

"We will stick with that roadmap," Rasmussen told Fox News.

He added that the Taliban is "under pressure everywhere" and he's "optimistic" about keeping to the transition timetable.

The affirmation comes as some lawmakers renew calls for an accelerated U.S. withdrawal from Afghanistan in the wake of the bin Laden killing. A bipartisan group of lawmakers introduced a bill last week calling for this, demanding a new timetable from the president within 60 days. Rep. James McGovern, D-Mass., one of the sponsors, said it no longer makes sense to keep more than 100,000 troops in Afghanistan now that bin Laden is dead and "Al Qaeda is scattered around the globe."

Sen. Richard Lugar, R-Ind., also said in an interview Sunday that the U.S. should "think very carefully about our objectives" in Afghanistan considering the toll it is taking on the military and budget.

"I would like to see the administration define this much more precisely as opposed to the fact that we're simply going to have a general review and 2014 is out there in some fashion," he said on CNN's "State of the Union." "And many members of Congress think that won't be the end of it. We'll be supporting the Afghan army indefinitely on our budget, on our time."

With bin Laden dead and President Obama about to change up the leadership of his military and intelligence teams, the administration is bound to look at the war in Afghanistan from a new perspective.

Asked about the possibility of reassessing the strategy in Afghanistan, White House National Security Adviser Tom Donilon told "Fox News Sunday" the pace of withdrawal will be decided based on "conditions going forward."

"Those decisions have not been made," he said. Donilon said a key U.S. goal is to ensure Afghanistan does not again become a "safe haven" for terror networks like Al Qaeda.

Sen. John Kerry, D-Mass., said lawmakers should look at whether the U.S. can accomplish the mission in Afghanistan with fewer troops.

"I think we have the ability to have a different footprint and still accomplish our goals," Kerry said on CBS' "Face the Nation." He also suggested the killing of bin Laden could open the door to the kind of "political solution" he says is necessary to end the war.

But former Vice President Dick Cheney, on "Fox News Sunday," cautioned that the U.S. does not need to "run for the exits" now that bin Laden is dead.