Indigenous Affairs Minister Amanda Vanstone says the Federal Government's plans to abolish the Aboriginal and Torres Strait Islander Commission (ATSIC) will not be sped up.

The Coalition has won control of the Senate, which must approve the legislation.

The Coalition senators who won seats in the recent election will not take up their positions until July 1, after which they will have the numbers to control the Senate.

Until then, the current Senate remains in place.

Labor, the Greens and independent senators have the power to unite and frustrate the Government's bid to push through legislation to abolish ATSIC.

The Coalition's plans to abolish ATSIC are currently before a Senate select committee, which is expected to report its findings around mid-November.

Under the proposed legislation, the ATSIC board would be the first to go with its regional councils to follow 12 months later.