Websites flouted the gag order and made the arrest of political activist Amir Makhoul into a rallying cry for critics of Israel's treatment of its Arab minority.
Israeli police spokesman Micky Rosenfeld said the gag order was imposed to avoid harming the investigation.
Israel's Shin Bet intelligence agency said in a statement that the men were arrested for "severe security offenses including contacting a Hezbollah agent." Additional details of the case are still subject to the gag order, the statement said. The two men have not been charged.
In recent years, several Israeli Arabs have been arrested for spying for Hezbollah, a fierce enemy of Israel suspected of involvement in bloody attacks against Jews outside the region as well. In 2006, Hezbollah and Israel fought a monthlong war, and Israel's president recently accused the militants of obtaining Scud missiles from Syria.
Makhoul, brother of a former member of Israel's parliament, was arrested last week. Makhoul heads Ittijah, a network for Arab organizations in Israel. Makhoul is a political activist known for expressing pro-Palestinian views, but he is not known to have advocated violence. Ittijah said Makhoul was arrested in a pre-dawn raid on his house in the northern city of Haifa on Thursday.
The other suspect in the case, Omar Sayid, was arrested April 24.
Adalah, an Arab legal center in Israel, is representing both suspects. "This is an effort to criminalize open political and social activity of political activists," Abeer Baker, an Adalah lawyer involved in the case, told The Associated Press. "If I have coffee with someone and he has certain political activities, it's as if I met him because I want to harm state security," she said.
Baker said Makhoul has not been allowed to meet a lawyer, and Sayid rejected the accusations.
"He clearly said that he denies all the charges and clarified to investigators that, yes, he has relations that are legal and not hidden, and that he doesn't belong to any cell or organization or anything like it," Baker said.
Arabs make up about 20 percent of Israel's 7.5 million citizens. They enjoy full rights but complain of decades of discrimination. Their communities are far below average economically and educationally.
Israeli Arabs have always had an uncomfortable position in a largely Jewish state. Most have relatives among Palestinians in the West Bank and Gaza, including many who fled or were driven out during the war that followed Israel's creation in 1948 and became refugees.
During the past 15 years, marked by long periods of intense Israeli-Palestinian violence, many Israeli Arabs have become radicalized, backing Palestinian demands for a state and criticizing Israeli moves against Palestinians.