Parliament is expected to pass the levy within weeks, establishing a secure funding base for the most important social and economic reform achieved by federal Labor.

In a second day of political brinkmanship over the NDIS, Mr Abbott blinked on Thursday in the face of a prime ministerial challenge to either back a new $3.3 billion levy in Parliament or fight an election on the issue. His conversion came after tense overnight talks within the shadow cabinet.

Coalition strategists weighed up the competing political costs of, on the one hand, surrendering a potent line of attack on Labor over rising taxes against, on the other hand, being seen to block a popular reform their leader had strongly supported.

Declaring ''we do want to see this come into the Parliament in this term'', Mr Abbott offered qualified support for enabling legislation and called for its immediate introduction.

''We are prepared to consider supporting a modest increase in the Medicare levy to make sure that this happens as soon as possible,'' he said.

''There are five weeks of parliament remaining, and I don't see why we can't get this dealt with so that this Parliament does have a substantial monument. This is not a day to be quibbling over something which is very, very important to the future of our country.''

Ms Gillard, who had weathered criticism for proposing the levy after previously rejecting it on principle, welcomed the announcement and moved quickly to reinforce the similarity of the Abbott manoeuvre.

''On the basis of that change of mind by the Leader of the Opposition, I will bring to the Parliament the legislation to increase the Medicare levy by half a per cent,'' she said.

It is likely the Federal Parliament will pass the levy by next month allowing it to commence from July 1, 2014.

The Coalition's change of heart, however, came with conditions - Mr Abbott demanded information on how the NDIS scheme would be funded beyond the revenue raised by the levy. He has also demanded more details of the eligibility criteria, amid fears that disabilities including levels of autism, deafness, and mental health might leave some families out in the cold.

However, Ms Gillard said the NDIS, now called DisabilityCare, would be fully funded by the levy in its start-up phase during which more funds would be banked in a special fund for later expenditure on the scheme.

The opposition also called for more information on the scope of the program. ''It's very important for the government to say precisely who it is proposing to cover,'' Mr Abbott said. ''Are people with autism in or out? Is vision impairment in or out and to what extent is it in or out? Is hearing impairment in or out? Mobility assistance, to what extent is that covered? These are all very important questions.''

Ms Gillard said the eligibility criteria were contained in the legislation passed by Parliament in March.