Criticism erupted last week following reports that Richard Foster was warned he would be fired if he told lawmakers about his cost estimates, which were higher than those Congress used when debating the bill. The higher estimates could have doomed the measure, which Congress narrowly approved in November.
White House spokesman Scott McClellan endorsed Thompson's plans to investigate the matter.
"Obviously it's a serious allegation," McClellan said.
Thompson said Tuesday his staff is gathering the documents.
"There seems to be a cloud over this department because of this. We have nothing to hide, so I want to make darn sure everything comes out," Thompson said.
In an hour-long meeting Tuesday with reporters, Thompson did not dispute the thrust of an Associated Press story reporting that in June then Medicare chief Thomas Scully threatened to fire Foster if he released his calculations to Democrats.
Scully has characterized his comments as "heated rhetoric in the middle of the night."
Foster estimated in June that a version of the Medicare bill similar to what became law would cost $551 billion, according to a document obtained and released by House Democrats.
The Bush administration projected in the budget submitted to Congress last month that the ten-year cost of the bill would be $534 billion, instead of $395 billion estimate used in writing the legislation.
Democrats applauded Thompson's request, but Sen. Edward Kennedy, D-Mass., said questions still remain about why the president, Thompson and other officials maintained the legislation would cost some $400 billion "when their best estimate was that it would cost much more."
Nine Republican members of the House had stated before final congressional approval of the legislation that they would not support a bill that cost more than $400 billion. The House approved the bill in a 220-215 vote.
Thompson said many lawmakers knew the administration's estimates of Medicare costs were higher than what the Congressional Budget Office calculated.
"I don't believe there was any obfuscation," Thompson said.
He also told reporters he never instructed Scully to prevent Foster from sharing his estimates with lawmakers.
Scott Whitaker, Thompson's top aide, said he telephoned Foster in June at Thompson's request to reassure him his job was safe.
The secretary placed much of the responsibility for the controversy on Scully.
Thompson told reporters he should have exercised more control over Scully. "But all of you know Tom Scully. Do you think that's possible?" Thompson said of the former hospital trade association executive known for his impulsive comments.
Rep. Pete Stark, D-Calif., told The New York Times that since Scully left government work in December, he was an easy scapegoat and the "perfect fall guy."
In an interview with The Washington Post on Tuesday, Scully said, "They can investigate till the cows come home, but I think I was right." He also repeated his past assertion that he had merely joked about firing Foster and that he only once had kept him from promptly responding to a Democratic request.