Court papers say Kadish's spying took place between 1979 and 1985, although he is alleged to have maintained contact with an Israeli official until this year.
US authorities also accused Kadish, who was arrested on Tuesday, of illegally acting as an agent for Israel from 1979 to 2008 without notifying the US attorney-general's office.
Kadish was suspected of reporting to the same Israeli official as former Pentagon official Jonathan Jay Pollard, who plead guilty to spying for Israel in 1986 and is serving a life term.
Washington registered its concern over the affair with its main Middle East ally.
"We would expect that Israel would not be engaged in such activities," Tom Casey, a US state department spokesman said.
The office of Ehud Olmert, the Israeli prime minister, which is responsible for the Mossad intelligence service, declined to comment.
But Danny Yatom, a legislator and a former head of Mossad, said the current case had angered Washington.
"I think what primarily bothers the Americans is the feeling that Israel didn't tell them the whole truth two decades ago, in 1985, when the Pollard affair exploded," Yatom told Israeli Army radio.
"The Americans asked if there are additional people that Israel ran or are running in the United States.
"The answer, to the best of my knowledge, was always no," Yatom said.