Washington (CNN) - Senators from both parties expressed shock and dismay Tuesday at the shooting of Afghan civilians by an apparent rogue American soldier this weekend, but most said the tragic incident should not lead to a change in the current U.S. policy that has combat troops withdrawing from the country by 2014.
"I support the policy the administration has laid out to move toward a transition over the next couple of years," said Sen. Mitch McConnell, the Republican leader from Kentucky who is often critical of Obama administration policies. "It certainly has been a very difficult period with the incidents that have brought this all so much to home again. I still think, though, it's important to remember the reason we went there and what happened when the Taliban was running the country."
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Senate Majority Leader Harry Reid, D-Nevada, agreed: "I think we should stick by what we have. We're drawing down in Afghanistan and we should stick by the timeline."
Senate Armed Services Committee Chairman Carl Levin, D-Michigan, said the "emotional impact" of the shooting, which killed 16 people including many children, will "reinforce" for many lawmakers and many Americans that the U.S. should continue troop reductions at the current pace.
"That position, to continue reductions at a steady pace, was aimed at keeping the pressure on for the transfer of responsibility to the Afghan army," which would then be strong enough to prevent the Taliban from reasserting itself across Afghanistan, Levin said.
"Obviously, it has hurt American support," Sen. John McCain, R-Arizona, who has long opposed the administrations' timeline for withdrawal. "If the Taliban takes over, the record is that they have cooperated and worked with al Qaeda and we want to avoid that happening."
"The president's continued discussion on withdrawals, the pace of withdrawals, sends the wrong message," McCain said. "The message is to the leaders in the region, including (Afghan President Hamid) Karzai, 'we're leaving.' They have to stay, they have to accommodate because they can't leave the region."
Sen. John Kerry, D-Massachusetts, the chairman of the Foreign Relations Committee, said there are indications the Afghan people are not responding with the same emotional anger they did following the recent apparently accidental burnings of Korans by American troops.
Explaining why-Kerry maintained: "It's tragic to say it but a little bit is the day-to-day cost of war that they've lived with for years and the fact that civilians have been killed in one instance or another by a bomb, by their bomb, by someone else's bomb, by someone going nuts. So this news is not quite as jarring under those circumstances as was the burning of the Koran."
Kerry said it's critically important that the U.S. military moves quickly and transparently to bring the accused soldier to justice. But he said the incident shouldn't impact President Obama's timeline for withdrawal.
"The president is on a pretty steep rate of withdrawal that the military has agreed to but I think anything beyond that the military would push back very significantly," he said. "You have to look at the mission. What is the mission? The mission didn't change overnight just because some guy went out and regrettably created mayhem."
Sen. Joseph Lieberman, I-Connecticut, said the U.S. should not go into "panic mode" because of the incident.
"I think the Afghan people generally and the Afghan government continues to want us to be involved," he said.
"A lot of service has been given, a lot of lives have been lost. I don't want that all to be in vain, said Lieberman, who like McCain would prefer not to have hard deadline for pulling out combat troops. "It would be a mistake to just pick up and run and the consequences would be disastrous for the Afghan people first and also for the U.S.'s credibility."
Despite the general position of senators that U.S. policy shouldn't change, there were some critics from both parties who said the withdrawal should be accelerated.
"I think this raises a lot of questions and my inclination is that we should be leaving Afghanistan more quickly," said Sen. Max Baucus, D-Montana, who has urged the U.S. to scale back its mission in Afghanistan after Osama bin Laden was killed. "I think we could accelerate it significantly."
"We won the war. We toppled the Taliban. We got rid of Osama bin Laden. Now we have an ally that disrespects us, who disparages us, who is openly confrontational to us," said Sen. Rand Paul, R-Kentucky. "I think at this point it's time to come home."