The Australian Greens have called on the government to increase the powers of the newly appointed Independent National Security Legislation Monitor.

Australian Greens spokesperson for legal affairs Senator Penny Wright said the Monitor needed greater funding and scrutiny powers to oversee the Abbott Government's massively expanded national security framework.

"The announcement of the new Monitor is long overdue and very welcome - but we now need to boost the position's powers to make sure it's more than a toothless tiger," Senator Wright said.

I am pleased to rise and speak to this important bill, which I have introduced with the aim of preserving and enhancing the crucial role of the Independent National Security Legislation Monitor (INSLM).

In a world characterised by unrest and fragile peace, the Australian Greens understand the need to have a robust conversation about our national security laws. We also have the highest regard for human rights and freedoms.

Australian Greens spokesperson for legal affairs Senator Penny Wright will today introduce a new Bill to increase the powers of the Independent National Security Legislation Monitor.

Earlier this year, the Abbott Government was defeated in its bid to scrap the Monitor - which plays a crucial role in assessing counter-terrorism laws - but the position remains vacant and unfunded.

"The position has been vacant since April, while bill after bill has been rushed through Parliament without proper scrutiny," Senator Wright said.

Debate was gagged on the Foreign Fighters legislation in the Senate before all aspects of the bill were explored, says Australian Greens spokesperson for legal affairs Senator Penny Wright.

"Labor and the Coalition have combined to rush the Foreign Fighters bill through the Parliament," Senator Wright said.

"Never mind that these are the most significant counter-terrorism laws in our lifetime, Tony Abbott and Bill Shorten have found a unity ticket on bad process and bad legislation.

Comment from Australian Greens' spokesperson for legal affairs Senator Penny Wright on news the Abbott Government will adopt the recommendations of the Parliamentary Joint Committee on Intelligence and Security on the Foreign Fighters bill:

"The recommendations of the Liberal-Labor committee are not enough to save this from being a very bad bill that will trample on long-held civil liberties and democratic rights.

"The committee's recommendations are just tweaking around the edges - they do not fix the substantive problems of this bill.

The Australian Greens will not support no-go zones, the extension of preventative detention orders and the collection of biometric data at airports in the Abbott Government's Foreign Fighters legislation.

Australian Greens spokesperson for legal affairs Senator Penny Wright said the Greens would seek to delay debate on the second tranche of terror laws to allow time for further scrutiny, amid concerns even the government does not fully understand the extent of the powers they are creating.