Washington (CNN) -- Secretary of State Hillary Clinton said Tuesday that the United States and Egypt are "moving toward a resolution" regarding the prosecution of Americans and other nongovernmental organization employees accused of trying to stoke unrest in the country.
"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."
The trial -- which includes 16 Americans accused of fraud in Egypt -- got a brief start Sunday as intense behind-the-scenes diplomatic discussions simmered over the case.
Asked Tuesday if she felt the charges against the workers were legitimate, Clinton replied "no, I do not."
Three of the judges expected to preside of over the case submitted letters that expressed their intention to step down, forcing Egyptian authorities to reshuffle their judicial rotation, Abdel Moez Ibrahim, the head of Egypt's Appeals Court, said Tuesday.
Ibrahim said that the judges' reasoning was based on "critical feelings," and done for "personal psychological reasons." He did not elaborate.
The trial is scheduled to resume April 26.
The accused were detained as part of a crackdown on pro-democracy, non-government groups, which Egyptian officials say is part of a pattern of foreign interference stoking unrest.
The specter of pulling more than $1 billion in U.S. aid to Egypt over the prosecution is something the Egyptian government is "coming to understand," Clinton said Tuesday.
Out of the 43 defendants facing fraud charges, only 14 non-American workers showed up to court for a trial unfolding in the wake of the revolution that ousted former President Hosni Mubarak.
Clinton declined to discuss the details of the negotiations.
"I don't want to go making this a dramatic situation," she said.
The list of charges includes the unapproved conducting of political training and opinion polls -- and sending reports to the United States.
The workers are charged with operating in Egypt without being officially registered and receiving foreign funding.
Of the Americans charged, only seven are still in Egypt. Those in the country are all believed to be at the U.S. Embassy, though the Egyptian government has not asked for them to be turned over or to turn themselves in.
Among the Americans charged in the case is Sam LaHood, director of Egypt operations for the International Republican Institute and the son of U.S. Transportation Secretary Ray LaHood.
Journalist Mohamed Fadel Fahmy contributed to this report from Cairo.