"While I am glad President Obama has dropped his plan to abandon the region entirely, if he is truly committed to fighting terrorism and securing a stable Afghanistan, he shouldn't shortchange what our military commanders have said they need to complete the mission," former Florida Gov. Jeb Bush said in a statement.
Also in a statement, South Carolina Sen. Lindsey Graham called Obama's decision one "that will require our men and women in uniform to accept an incredibly high risk, with little support, simply because he's the president who promised to end wars."
Graham added that he would have a different strategy as commander-in-chief.
"As president, I will follow the advice of my commanders and require a conditions-based withdrawal -- not an artificial timeline," he said.
Graham elaborated on his statement in an interview with CNN's Jake Tapper on Thursday, saying that Obama didn't listen to advice from military commanders.
"I'm telling you he's picked a number that's not militarily sound. He intentionally ignored all military advice to keep a residual force in Iraq," Graham said. "He paid a price and this 5,500 number is not a militarily sound number."
Former Arkansas Gov. Mike Huckabee attacked Obama's decision on social media, tweeting, "Our heroes deserve more than political pandering and empty promises by @POTUS."
"The American people deserve justice, dignity & closure," Huckabee continued. ".@POTUS' embarrassing address today and his equally embarrassing Afghanistan strategy offer neither."
Kentucky Sen. Rand Paul told CNN's Wolf Blitzer that the U.S. mission in Afghanistan has swelled to a level well beyond the intention in 2001 to bring Osama bin Laden to justice and prevent Afghanistan from being a safe haven for terrorists.
"I think it's a mistake. It's also not what our founding fathers intended," he said.
Paul added, "I think people will not stand up and defend themselves until they're asked to."
Carly Fiorina said she supported Obama's "recognition of reality," but criticized the President for not listening to military commanders.
"He didn't listen," Fiorina told reporters after a town hall event in Iowa. "He thought he knew better. So (as President) I'm going to start by talking to our military commanders about what is it that needs to be done to ensure the Taliban and ISIS do not take over that country."
Not all of the reaction from Republican 2016 hopefuls was negative. Ohio Gov. John Kasich said the President's decision was "wise."
"Now that the situation has deteriorated on the ground, I think it's a wise decision to say we're just not going to just go running out of there and lose all the things that we had invested over the years," Kasich told reporters in Nashua, New Hampshire.
New Jersey Gov. Chris Christie took a similar stance, telling Michael Smerconish on his SiriusXM radio show that although he would have taken a different approach to Afghanistan from the beginning, "I think it's the right thing to do."
Former Pennsylvania Sen. Rick Santorum tweeted his support for Obama's decision, saying that the president "has learned his lesson from removing troops in Iraq that led to ISIS."
And Florida Sen. Marco Rubio said in a statement that although he "welcomed" Obama's decision, he did not agree with "his decision to prematurely announce a further drawdown before he leaves office. Our presence in Afghanistan should be dictated by battlefield conditions, which are impossible to predict more than a year in advance."
The decision to maintain 9,800 troops in Afghanistan until nearly the end of Obama's time in office comes after months of discussions with Afghanistan's president, Ashraf Ghani, and the nation's CEO, Abdullah Abdullah, senior administration officials said Wednesday night. Obama also consulted with U.S. military commanders on the ground in Afghanistan as well as his entire national security team, officials added.
According to the new White House plan, the number of U.S. military personnel in Afghanistan would drop to 5,500 by early 2017, as Obama prepares to leave office. At that point, U.S. forces would be based in the Afghan capital of Kabul, as well as in military installations in Bagram, Jalalabad and Kandahar.
"Afghan forces are still not as strong as they need to be," Obama said in making the announcement.