The Daily Mirror newspaper reported last week that a secret British government memo said Blair had talked US President George Bush out of bombing the Arab broadcaster's Doha headquarters in April 2004.
The White House has dismissed the report as "outlandish", while Blair's office has so far refused to comment.
Blair was asked in a written question to parliament made public on Monday "what information he received on action that the United States administration proposed to take against the Aljazeera television channel?"
In a written response, Blair gave the one-word answer "none".
The question, published on the parliament website, was proposed for discussion by lawmaker Adam Price, of the Welsh party Plaid Cymru.
A spokeswoman for Blair's Downing Street office made no further comment on the prime minister's response.
At a London news conference late on Monday, Daily Mirror's associate editor Kevin Maguire said he did not believe the reported threat against Aljazeera was a joke.
"It is clear from the language used in the memo and its context that Tony Blair took it seriously and counselled against it. It certainly wasn't a joke," he said.
Aljazeera chief Waddah Khanfar
wants an explanation from Blair
The paper quoted an unnamed government official as suggesting Bush's threat was a joke, but had another unidentified source saying the US president was serious.
Aljazeera's general manager Waddah Khanfar, who flew to London last week to seek an explanation about the memo, said he was unsure what to believe, but Aljazeera would not abandon the story until it got an answer.
"I want not to believe it," he said.
Britain's attorney-general has warned other media that they can be prosecuted under the Official Secrets Act if they reveal further details of the memo.
Britain is prosecuting a civil servant and a parliamentarian's aide for leaking the secret document.
The Mirror's report was picked up by the world's media and prompted Aljazeera to demand clarification from the US and Britain.