Downing Street communications director Alastair Campbell and the prime minister's chief of staff, Jonathan Powell, have both been invited to go before the Committee for Standards in Public Life.
Until now neither have attended the inquiry, which is focusing on relations between ministers, officials and political advisers.
But veteran MP Tam Dalyell is hoping to press the issue by tabling a Commons question urging Mr Blair to to instruct the pair to give evidence.
Committee chairman Sir Nigel Wicks had been set to ask the two political aides about the extra powers that enable them to manage civil servants.
'Reluctant' guests
Mr Dalyell, Father of the House of Commons, said: "I am surprised that Mr Campbell and Mr Powell have declined to give evidence.
"Is it with the prime minister's authority that they decline to appear?
"In the interests of transparency these epicentral figures in the government ought to be required to give their point of view.
"I cannot understand Downing Street's reluctance for them to do so."
A Downing Street spokesman said that these officials did not generally appear before such committees.
Jo Moore
The number of special advisers, used to develop policy and media strategy, has more than doubled under the Labour government and their salaries now cost £4.4m.
Sir Nigel said the inquiry would look to see if the key players in government were working together for the "public good".
The controversy over Jo Moore, the former transport special adviser who suggested 11 September was a good day to "bury" bad news has pushed such questions into the limelight.
Sir Nigel has said that three yardsticks would be used in the committee's investigation:
The government has promised to introduce a Civil Service Act to protect the independence of civil servants.
That will be something considered by the committee, who want to have their say on what checks and powers such legislation should include.
A range of former and present special advisers, academics and political commentators have been invited to give their views.