The federal government's decision to commit $3.5 billion in funding for Australia's largest tollroad project, WestConnex, will be the subject of Auditor-General investigation.

Following pressure from the Greens and Labor, the National Audit Office will scrutinise whether the Coalition government received appropriate advice and value for money in committing $1.5 billion in direct funding to the project in Sydney's west, as well as a further $2 billion as part of a loan agreement with the NSW government.

To be built in three stages, the 33-kilometre motorway project relies on funding from both the federal and state governments, as well as on tolls from motorists.

Both Labor and the Greens have claimed credit for the Auditor-General's decision to investigate the federal funding.

Anthony Albanese, the federal opposition spokesman on transport and the sitting member for the inner-city seat of Grayndler, said Labor had repeatedly raised concerns about the Coalition government's advance payments for large projects such as WestConnex without assessment by Infrastructure Australia, or the finalisation of business cases.

"That was a direct breach of the Liberals' 2013 election promise not to fund major infrastructure projects without the finalisation of cost-benefit analysis," he said.

As federal transport minister, Mr Albanese offered $25 million for planning of the motorway.

In the 2013 federal budget he also promised up to $1.8 billion for the M4 and M5 motorway components of WestConnex but imposed three conditions. These were the completion of a detailed business case, that the motorway provide a direct link to central Sydney and Port Botany, and that new tolls should not be imposed on existing roads.

Federal Major Projects Minister Paul Fletcher accused Mr Albanese of a backflip on WestConnex following his promise as transport minister to part fund the project.

"This is a troubling pattern from the Labor Party – to stop their voters shifting to the Greens, we're seeing Labor start to oppose critical infrastructure," he said.

Mr Albanese faces a tight contest in his inner Sydney electorate with Greens candidate Jim Casey. The pair will speak at a forum on WestConnex in Balmain on Thursday night.

Mr Casey said proper processes were not followed in the federal funding for WestConnex, adding that both the Liberals and Labor had promised money for the project during the 2013 election campaign.

The Auditor-General, Grant Hehir, confirmed in a letter to the Joint Committee of Public Accounts and Audit on April 28 that he would request an investigation into the Commonwealth funding approvals and decisions taken for WestConnex.

His confirmation followed a resolution moved by Greens Senator Scott Ludlam in the Senate in February.

As the former NSW auditor-general, Mr Hehir released in late 2014 a report into WestConnex that concluded: "It was not able to form a view on whether the project is a worthwhile and prudent investment … for the NSW government."

WestCONnex Action Group spokeswoman Pauline Lockie said Mr Albanese was "oscillating wildly" between claiming credit for the Auditor-General's decision to scrutinise funding and "saying that there is nothing at federal level he can do to stop WestConnex if Labor is elected".

Ms Lockie said the investigation was needed to bring transparency to the project because costings had been redacted from a business case released by the Baird government.

NSW Planning Minister Rob Stokes has approved the first and second stages of the $16.8 billion project. Demolition of houses compulsorily acquired for the first stage began several weeks ago.

Roads Minister Duncan Gay said he welcomed the Auditor-General's involvement even though WestConnex had received approval from Infrastructure NSW and Infrastructure Australia.

"You can do all the reports in the world, but you need only ask the people stuck in traffic on the M4 and M5 every day how important this project is," he said.

Meanwhile, Prime Minister Malcolm Turnbull has promised $50 million in funding for improvements to Appin Road – a major link between south-western Sydney and the M1 north of Wollongong – if re-elected.

The 37-kilometre stretch of road has earned a reputation as one of NSW's most unsafe in recent decades. Between 2000 and 2015, 23 people died in 22 serious crashes on Appin Road.

Under the Coalition's election promise, the link on which up to 12,000 motorists travel each day will be improved to allow for better separation between vehicles and larger road shoulders.

with James Robertson