The Senate has set up a probe into the Coalition’s $4.8bn urban congestion fund including the role of the prime minister’s office in the commuter car park controversy.

The upper house on Tuesday agreed to a Greens motion to refer the matter to an inquiry following a scathing auditor general’s report into the $660m car park fund that found projects were handpicked by the government on the advice of Coalition MPs and candidates.

Labor and the Greens have continued to pursue the government over pork-barrelling in marginal electorates after revelations the same staffer in the prime minister’s office was involved in both the sports rorts scandal and the selection of car park projects.

The former urban infrastructure minister, Alan Tudge, has claimed he was unaware of a “top 20 marginals” document the auditor general found was used to determine which MPs and candidates to canvass regarding the location of proposed car parks.

Scott Morrison has so far refused to answer questions about his involvement – refusing to say whether he had seen the document but explaining “the ministers”, Tudge and former infrastructure minister Michael McCormack, were responsible for project selection.

On Tuesday, a motion by Greens senator Janet Rice for an inquiry by the finance and public administration references committee was approved by the Senate, with no division called by the government to test support.

The inquiry will consider whether the urban congestion fund “meets the highest standards of governance, performance and accountability in the expenditure of public funds”. The parliamentary inquiry will have a broader remit than the Australian National Audit Office allowing it to examine road projects in addition to the car parks.

The inquiry will also consider “the role of the offices of the minister(s), the prime minister and deputy prime minister, and any external parties, in determining which projects to allocate funding and who would announce these projects”.

The ANAO found 77% of the car parks funded by the government were in Coalition-held electorates and a further 10% were in six non-Coalition held electorates where Coalition candidates’ views were canvassed.

Rice said in a statement it appeared the Coalition had engaged in a “coordinated, systematic, multibillion-dollar scheme to buy votes at the last election”. “Australian taxpayers deserve to know how their money was spent,” she said.

Morrison last week defended the commuter car park fund, claiming that Australians were the “winners” from the program.

In question time on Monday, Morrison said that the “normal processes” were followed with the expenditure review committee approving funding for projects selected by ministers.

On Tuesday, Labor MP Peta Murphy asked how Morrison could claim Australians were the winners given the Coalition had so far only delivered two of 47 commuter car parks promised in the run-up to the 2019 election.

The urban infrastructure minister, Paul Fletcher, noted the government had committed additional funding to build a car park at Frankston in her electorate “as we recently discussed when she came to my office to raise this issue”.

Fletcher accused Labor of having a “very confusing” and “mystifyingly schizophrenic” position on commuter car parks because it had promised to fund a slate of projects before the last election including 11 that the Coalition also promised to build. “But our position is consistent, we’re getting on with delivering commuter car parks,” he said.

Fletcher cited Ferny Grove in Queensland as another car park site that had recently started construction.

The federal court on Tuesday held a hearing in a bid by Beechworth Lawn Tennis Club to compel the release of documents that may illuminate the role of the former sport minister Bridget McKenzie in the $100m community sport infrastructure grant program.

In January 2020, the ANAO found the sports grants program had been skewed towards target and marginal seats by a parallel assessment process conducted in McKenzie’s office. McKenzie and the government deny any wrongdoing.

Beechworth is seeking correspondence between McKenzie and Sport Australia, hoping to prove that the agency inappropriately delegated its power to select grant recipients to the minister or acted under her direction.

Sport Australia resisted the application, arguing that only documents relating to the approval of the Beechworth grant are relevant. Sport Australia claims McKenzie requested grants but did not provide final approval for them.

Justice David O’Callaghan reserved his decision on the documents.