Gen. Dempsey: Taliban will be a fixture in postwar Afghanistan

While the Afghan National Security Forces (ANSF) have made significant progress in former Taliban strongholds in the southern and eastern part of the country, the terror group will remain a problem for Kabul.

"There will be contested areas, and it will be the Afghans' choice whether to allow those contested areas to persist, or, when necessary, take action to exert themselves into those contested areas," Dempsey said..

The four-star general's comments echo those of Marine Corps Gen. Joseph Dunford, the top U.S. officer in Afghanistan.

Despite the gains made by the ANSF, the insurgency's resiliency and steep learning curve still facing the country’s nascent military is raising serious questions on whether the Taliban can be completely flushed out of Afghanistan.

"My assumption is that the [Afghan] insurgency will still exist after 2014," Dunford said in an interview with ABC News on Monday.

"The conditions are not yet set for a stable and secure Afghanistan in the long-term," he added during his first interview since taking over the top spot in the country in February.

That resiliency was on full display on Saturday, during Dempsey's two-day visit to the country.

The chairman's trip was to assess the ongoing effort to end America's war in the country within the next year.

On Saturday, six U.S. soldiers, a Defense Department official and an American foreign service officer were killed in a spate of attacks and suicide bombings in eastern and southern Afghanistan.

A Taliban suicide bomber struck a State Department convoy and its military escort as they were delivering books to a school in Zabul province in southern Afghanistan.

In Eastern Afghanistan, a U.S. soldier was killed during combat operations against Taliban forces in the country.

"There are American and Afghan casualties. We are still investigating the incident and cannot confirm details at this time," according to a statement by the U.S. embassy in Afghanistan issued on the day of the attacks.

U.S. and NATO forces are in the midst of what will likely be the final fighting season for American troops before the White House's withdrawal deadline of 2014.

The 66,000 American troops still in Afghanistan are preparing to pull out of the country this spring. The final group of those U.S. forces is expected to leave the country next April.