Sixty years after the end of the Korean war, the United States and South Korea still can't agree on who should take charge if another war breaks out with the communist neighbour to the north.

For years, Washington has been trying to persuade the South Korean military to take operational control of its own forces in wartime, ending a six-decade arrangement during which US commanders have retained that authority over South Korean troops. Although supportive in principle, a succession of governments in Seoul has repeatedly delayed the command transfer, reinforcing doubts about whether the South Korean military is capable of operating without US leadership.

Previous deals that would have transferred wartime command of South Korean troops to Seoul in 2009 and 2012 fell by the wayside. Now the latest timetable – to transfer control to the South Korean military by December 2015 – has become infected with doubt as South Korean leaders have expressed anxieties again about their ability to command their troops in the face of threats from an increasingly unpredictable North Korea.

South Korean officials began a public campaign this summer to request another delay beyond 2015 but haven't specified a new date. US officials have not agreed to any changes so far. Some have said they are becoming frustrated with South Korea's reluctance to take charge of its own defence.

Last week, defence secretary Chuck Hagel travelled to Seoul for three days of talks. But he told reporters accompanying him that he doubted that the thorny issue could be resolved during the visit.

"We're constantly re-evaluating each of our roles," Hagel said. "That does not at all subtract from, or in any way weaken, our commitment."

In a reminder of how a sudden outbreak of war remains a constant threat, Hagel toured the demilitarised zone, the 4km-wide buffer that divides North and South Korea and is the most heavily guarded border in the world.

There are 28,500 US troops permanently stationed in South Korea. That's a fraction of the size of the South Korean military, which has 640,000 personnel. The South Korean government, however, considers the US military presence a crucial deterrent, and some South Korean officials worry that a lessening of the US role could embolden North Korea.

North Korea's recent hostile rhetoric and military brinkmanship have added to those concerns. In February, North Korea conducted a nuclear test, two months after testing a long-range ballistic missile that could potentially strike the western United States. Memories are also fresh here of a March 2010 incident in which North Korea torpedoed a South Korean naval vessel, killing 46 sailors.

The question of who would take command of joint US-South Korean forces during another Korean conflict is an unresolved hangover from the cold war.

South Korea has wielded command of its troops during peacetime since 1994 and has steadily upgraded its military capabilities. But the US armed forces remain better equipped to deal with the threat of nuclear, ballistic missile or cyber-attacks.

In May, South Korea first floated the possibility of keeping its forces under US wartime command beyond 2015. Since then, Seoul has become more vocal in stating its request.

In August, defence minister Kim Kwan-jin raised the issue with Hagel during a meeting in Brunei. Afterwards, Kim told the South Korean parliament that there was "a consensus" in his government that sticking with the December 2015 deadline was no longer "appropriate", according to the state-run Yonhap news agency. But he acknowledged that the Americans didn't necessarily agree.

Hagel met Kim and President Park Geun-hye during his most recent trip. Although the Obama administration is eager for South Korea to take permanent command of its own forces, US officials don't want to leave the impression that handing over control might weaken the US commitment to the region.

The Pentagon has said that it has no plans to scale back its troop presence in Korea. US forces on the peninsula would remain under US command.

Back in Washington, however, some members of Congress have grown tired of South Korea's reluctance to take charge of its own defence, especially at a time of US budget constraints.

"I believe it's important that we see to it that the primary responsibility for defending South Korea during a time of war lies with South Korea," said Senator Carl Levin from Michigan, the Democratic chairman of the Senate armed services committee, said during a July confirmation for the incoming commander of US forces in Korea, Army General Curtis Scaparrotti. "It is a sovereign nation, and sovereign nations should be responsible for their own national defence in time of war."

During his confirmation hearing, Scaparrotti said that he agreed with the December 2015 timetable and that he would "do everything possible to ensure that we stay on track".

But he left some wiggle room. In written responses to the Senate panel, Scaparrotti said the transfer of wartime command would be "conditions driven" and had to be "executed in a manner that does not accept any unnecessary risk to the national security" of South Korea.

This article appeared in Guardian Weekly, which incorporates material from the Washington Post