After what he called "a very good meeting" with Chinese Foreign Minister Tang Jiaxuan, Secretary of State Colin Powell sounded confident that Chinese officials are well on their way to setting free two jailed U.S. residents Goa Zhan and Qin Guangguang. 

The two are being held in Beijing on charges of spying for Taiwan, but critics of the Chinese regime say the lack of a transparent judicial system and due process in the communist nation cast doubt over the merits of the charges against them.

Powell is holding bilateral meetings with Chinese officials on the sidelines of the summit of southeast Asian nations in Hanoi, Vietnam. He is trying to get Beijing to release the two American residents — who are each facing 10 years in jail — as well as improve the treatment of several others who await trial.

"Several of these cases are now on the way to resolution on humanitarian grounds and you will see that in a quite obvious way within the next 24 hours or so," Powell said on Thursday in Vietnam.

Gao and her colleague, both of whom are still Chinese citizens but have permanent U.S. residency, applied for release based on medical conditions after the two were convicted Tuesday.

Chinese Foreign Minister Tang assured Powell that the appeals were being seriously considered, though Powell deferred elaboration on the cases to the Chinese.

But when a Chinese ministry spokesman was asked to elaborate, he denied hearing anything about movement "within 24 hours," saying only that the Chinese courts would consider the requests from these "proven spies" in due course.

The U.S. and China recently clashed over another Chinese-born academic, Li Shaomin. Although Chinese officials term him the "ringleader" of a "Taiwan espionage ring," Mr. Li, who is an American citizen, was expelled to the United States after his conviction.

"I am so glad to be heading home. I am looking forward to being reunited with my family and first of all I would like to thank our government for it great help and support," Li said.

Powell is expected to bring up the topic of the detainees again on Saturday when he visits Beijing after the conclusion of the Hanoi summit. He will have meetings at the highest level, including with president Jiang Zemin.

But as for what might be said in these meetings if Gao and Qin are still imprisoned when Powell arrives in two days, a senior state Department official would only say, "We'll see."

Fox News' Sharon Kehnemui contributed to this report