Washington and Cairo may soon end a standoff over 16 American civil society employees facing trial in Egypt, Secretary of State Hilary Clinton said as the case's judges recused themselves.

"We are engaged in very intensive discussions with the Egyptian government about finding a solution," Clinton said during a Senate hearing. "We've had a lot of very tough conversations, and I think we're ... moving toward a resolution."

Cairo is "coming to understand" Washington was serious when it threatened to cut off $1.55 billion in annual aid to Egypt, she said Tuesday.

When pressed for more information by Republican Senator Lindsey Graham, Clinton said she did not "want to go any further," but said, "We're hoping to resolve this very soon."