In broadcast interviews, Mullen wouldn't say whether more American forces troops would be needed. A large number of civilian experts is also required to help bring stability to Afghanistan's government and develop the economy.
The Obama administration is awaiting an assessment about the situation from the top U.S. commander in Afghanistan. That report is expected in about two weeks.
Just over 50 percent of respondents to a Washington Post-ABC News poll released this past week said the war in Afghanistan is not worth fighting.
Mullen, a Vietnam veteran, said he's aware that public support for the war is critical. "Certainly the numbers are of concern," he said. But, he added, "this is the war we're in."
Three years ago, the U.S. had about 20,000 forces in the country. Today, it has triple that, on the way to 68,000 by year's end when all the extra 17,000 troops that Obama announced in March are to be in place. An additional 4,000 troops are arriving to help train Afghan forces.
The new strategy is intended to disrupt and defeat al-Qaida, the Taliban and its extremist allies. These forces have become much stronger and use safe havens in Pakistan to hide and plan attacks, he said.
"I recognize that we've been there over eight years," Mullen said. "This is the first time we've ever really resourced a strategy on the civilian and military side."
Arizona Sen. John McCain, the top Republican on the Senate Armed Services Committee, said he wants the military leadership in Afghanistan to use the same aggressive approach that Gen. David Petraeus used successfully in Iraq.
He said the top U.S. commander in Afghanistan, Gen. Stanley McChrystal, should say exactly how many troops he needs in Afghanistan, let the Congress debate it and Obama would make the ultimate decision.
Troops in Afghanistan should "clear and hold" an environment for people so that economic and political progress can be made, he said. McCain said he worries McChrystal will be pressured to ask for lower troop totals than he needs.
"I don't think it's necessarily from the president," he said. "I think it's from the people around him and others and that I think don't want to see a significant increase in our troops' presence there."
On the question of what it will take to turn the tide in Afghanistan, McCain said: "I think within a year to 18 months you could start to see progress."
McCain acknowledged that public opinion on Afghanistan is slipping. But he said that opinion could be reversed.
"I think you need to see a reversal of these very alarming and disturbing trends on attacks, casualties, areas of the country that the Taliban has increased control of."
Mullen appeared on NBC's "Meet the Press" while McCain's interview Friday with ABC's "This Week" was aired Sunday.