The companies said the subpoenas came from a special grand jury investigating whether a figure in the Bush administration improperly disclosed the identity of the agent, Valerie Plame, after her husband, former diplomat Joseph Wilson, publicly challenged the White House's claim that Iraq had been trying to obtain uranium for nuclear weapons from Africa.
Wilson has charged that officials made the disclosure in an effort to discredit him.
Plame was first identified as a CIA specialist on weapons of mass destruction by syndicated columnist and TV commentator Robert Novak last July. Novak said his information came from administration sources, but has declined to name them.
NBC and Time said the subpoenas were aimed at Russert, the "Meet the Press" host and moderator, and Time magazine reporter Matthew Cooper, both of whom have reported on the Plame controversy.
Novak's office has declined repeatedly to say whether he has been subpoenaed or cooperated with investigators.
NBC News president Neal Shapiro said the Russert subpoena was misdirected because he was "not the recipient of the leak." The subpoena, he said, would have a "potential chilling effect" on the network's ability to report the news.
"The American public will be deprived of important information if the government can freely question journalists about their efforts to gather news," Shapiro said in a statement. "Sources will simply stop speaking to the press if they fear those conversations will become public."
Robin Bierstedt, a Time Inc. vice president and deputy general counsel, said the Time subpoena referred to two articles by Cooper and others, one on the Time.com Web site on July 17, 2003, and the other in the magazine's June 21, 2003 issue.
Time planned to file a motion next month asking that the subpoena be quashed, she said.
"It is Time Inc.'s policy to protect its confidential sources," she said. "While we would like all of our reporting to be on the record, a promise of confidentiality is sometimes necessary to get information that would otherwise be unavailable."
Patrick J. Sullivan, a special counsel in the grand jury inquiry, has repeatedly declined to comment on the case.
The allegation that Iraq possessed weapons of mass destruction was central to the White House rationale for invading Iraq in March 2003.
Wilson, who was the U.S. charge d'affaires in Baghdad at the onset of the 1991 Persian Gulf War, was dispatched to Niger in early 2002 to investigate a report that Iraq had tried to purchase yellow-cake uranium, which could be used to make a nuclear bomb.
He reported back that he saw no evidence of an Iraqi bid and doubted it could have succeeded.
The CIA told the White House it doubted that Iraq had sought uranium in Niger, but British intelligence included the Niger charge in a dossier laying out the case for war in late 2002.
In his January 2003 State of the Union speech, President Bush referred to the British report of the Niger allegation.
Days later, the International Atomic Energy Agency said documents purporting to be evidence of the Niger bid were forgeries. An FBI investigation is trying to learn who forged them.
Wilson went public with his findings in July 2003, prompting the White House to retract the Niger claim. After Wilson's revelation, Plame's name was printed in Novak's column.
Naming a clandestine agent could violate federal law. The CIA asked for an investigation of the leak, and the Justice Department agreed. Attorney General John Ashcroft recused himself from the case, and Fitzgerald took over.
Several top White House staff members have already testified before a grand jury in the case, including press secretary Scott McClellan, spokeswoman Clair Buchan, former press office staffer Adam Levine, former vice presidential adviser Mary Matalin.
A number of other current or former officials have been interviewed by the FBI, including top Bush political adviser Karl Rove, communications chief Dan Bartlett, former spokesman Ari Fleischer and Cheney spokeswoman Cathie Martin, said two sources who spoke on condition of anonymity.
The Post reports the FBI has also talked to Cheney chief of staff I. Lewis "Scooter" Libby, along with Levine, Matalin and McClellan.
The grand jury has also subpoenaed the records of phone calls from Air Force One, according to published reports.
Justice Department guidelines for criminal prosecutions state that all avenues should be explored before reporters are subpoenaed or approached in an investigation. The issuing of new subpoenas for reporters may indicate that the investigation is nearing an end.
Investigators earlier tried to encourage journalists to talk by asking White House staff to sign waivers freeing reporters of any promises of confidentiality. But according to The Post, most officials were advised by the lawyers not to sign, and did not.