WASHINGTON -- The United States and South Korea are negotiating a defense cost-sharing agreement that will be fully acceptable to both President Donald Trump and President Moon Jae-in, a US official said Thursday.

The two countries have been wide apart on how much Seoul should contribute to the cost of keeping 28,500 American troops stationed on the peninsula.

The US has demanded $1.3 billion a year -- a nearly 50 percent increase from last year -- while South Korea has refused to accept anything more than a 13 percent increase.

"It's recognized that we still need to get to a place that is fully acceptable for both governments, that is fully acceptable for President Moon, and for President Trump," R. Clarke Cooper, assistant secretary of state for political-military affairs, said during a virtual press briefing.

"But we're going to keep working this, and why? The main reason why is because our alliance is a tremendous investment, and both parties have a commitment toward the alliance," he said. "If anything, the commitment to our alliance is the bedrock of the negotiations. It allows for us to have a candid discourse about burden-sharing and shared responsibility. So, while there's a shared adversity that we face in the region, there's also shared responsibility of meeting that."

Trump rejected South Korea's latest offer, saying the country should "pay for a big percentage of what we're doing" there.

His initial request for this year's deal, or Special Measures Agreement, is known to have been $5 billion.

"From where we are in Washington, we've certainly seen ourselves as very flexible on being able to adjust as we proceed through the negotiations," Cooper said, apparently referring to that cutback.

"We are still communicating, and it has been a healthy back and forth," he added.

More than 4,000 South Korean employees with US Forces Korea have been placed on unpaid leave since early April due to the absence of a deal.

The US has dismissed South Korea's request to first settle the wages issue while they work out a comprehensive agreement.

On North Korea, Cooper said it would be "inaccurate" to say there are no confirmed cases of COVID-19 there, as claimed by Pyongyang. He didn't elaborate.

On whether the North has accepted US offers of assistance with the pandemic, he said he wasn't aware of that happening.

"I would say generally that there have been a number of states that have not accepted our offers, but I would caveat that there is a difference between an active non-acceptance and non-reply," he said. "The challenge with Pyongyang is they have not been as forthcoming -- not only to us, but to any other state in the world -- as to the true nature of what they're dealing with." (Yonhap)