WASHINGTON (Reuters) - Secretary of State Hillary Clinton said on Wednesday the United States cannot abandon Pakistan but that the South Asian nation must help solve Afghanistan's difficulties or it will "continue to be part of the problem."

Her comments were the latest in a series by U.S. officials exposing the difficulty of the relationship with Pakistan, particularly after Washington publicly accused its powerful Directorate of Inter-Services Intelligence (ISI) of supporting a militant attack on the U.S. embassy in Kabul on September 13.

The head of the ISI, Lieutenant General Ahmed Shuja Pasha, has denied the U.S. accusation.

The United States and Pakistan have bickered publicly since the former chairman of the U.S. Joint Chiefs of Staff, Admiral Mike Mullen, told Congress last month that he regarded the militant Haqqani network as a "veritable arm" of the ISI.

Answering questions after a speech sponsored by the Center for American Progress in Washington, Clinton said the United States had no choice but to work with Pakistan in trying to stabilize neighboring Afghanistan.

"This is a very difficult relationship but I believe strongly it is not one we can walk away from and expect that anything will turn out better," she said.

"Pakistan has to be part of the solution or they will continue to be part of the problem," she added. "And therefore, as frustrating as it is, we just keep every day going at it and I think we make very slow, sometimes barely discernible progress, but we're moving in the right direction."

Despite mounting exasperation in official Washington, dramatic change in U.S. policy looks unlikely in the short term toward Pakistan, an unstable, unpredictable nation that has nuclear weapons and controls a key supply route needed to keep U.S. troops fed and fighting in Afghanistan.

(Editing by Christopher Wilson)