"That really is the focus of effort over the next 18 months. That's why we need to start now — especially with the Afghan security forces — to talk about 2018, not 2014," the four-star general told the BBC.
"That period of time will allow these gains to be sustainable," he added.
White House officials had hoped to fast-track the Taliban peace plan, saying a deal would be "absolutely essential to bringing the war to a responsible close," Doug Lute, the administration's top adviser for South Asia, said in January.
But officials in Kabul have become increasingly frustrated with the struggling peace process, blaming interference from Pakistan for derailing those efforts.
Afghan President Hamid Karzai and others inside the Karzai administration claim Pakistan is already walking away from Afghan-led peace talks with the Taliban.
Islamabad canceled efforts, at the last minute, to fly Taliban representatives from the country to Doha to participate in the initial round of negotiations in March.
Islamabad's demand that Kabul cut all ties with Pakistan's long-time foe, India, as well as immediately sign a military cooperation pact with Pakistan was a clear sign that Islamabad was not ready to make a deal, Afghan officials said in March.
That said, there is little evidence to suggest Islamabad is intentionally undermining Afghan-led and American-backed peace talks with the Taliban, Dunford told Congress in April.
"I think we're waiting now for the Taliban to meet their end of the bargain in terms of moving the process ahead. But that's not a process that I'm deeply engaged in on a routine basis," Dunford told Senate Armed Services Committee members at the time.
Secretary of State John Kerry is planning to travel to Islamabad this month to meet with Pakistani Prime Minister Nawaz Sharif.
It will be Kerry's first trip back since Sharif assumed power in the country, Pakistani foreign ministry spokesman Aizaz Ahmed Chaudhry told reporters in Islamabad.
It remains unclear whether Kerry and Sharif will discuss the stalled peace process, but the visit comes as the Taliban has stepped up their attacks in Afghanistan.
Taliban insurgents detonated a massive car bomb in downtown Kabul on Tuesday, in what Afghan security officials claim was an attempt to kill members of the country's supreme court.
Roughly 17 civilians were killed and 40 were critically wounded when the explosive-laden sport utility vehicle blew up in a busy intersection in downtown Kabul, according to recent reports.
On Monday, Afghan military and police repelled a coordinated Taliban attack against the main airport in Kabul, ending with the deaths of seven insurgents.
Waves of Taliban gunmen and suicide bombers assaulted the airport, looking to breach the military side of the facility that serves as headquarters to International Security Assistance Force (ISAF) Joint Command, according to recent reports.
At no time was the ISAF side of the airport breached, and no American or NATO troops were killed in the ensuing gun battle, a command official said at the time.