Fremantle MP Josh Wilson said he wasn’t convinced about whether Australia needed the new submarines.

“I’m not completely convinced that nuclear-propelled submarines are the only or best answer to our strategic needs,” he told parliament on Monday night, noting he wasn’t privy to private security briefings.

“The AUKUS agreement, arrived at with some characteristically questionable secrecy by the former government … is not a sports team of which we have all suddenly become life members.”

Wilson also questioned how nuclear fuel would be disposed of, noting the UK and US had struggled to deal with their decommissioned boats properly.

Three Labor MPs asked Albanese questions about the deal at a caucus meeting in Canberra on Tuesday.

However, Michelle Ananda-Rajah, who was one of the MPs who asked about the deal, has since come out saying, “I fully support the government’s AUKUS plan”.

Media reports suggest the second MP was Libby Coker.

The questions related to workforce issues, cost and how Australia would retain its sovereignty. They included concerns from constituents.

Opposition defence spokesman Andrew Hastie said the prime minister needed to unite his caucus if he wanted to succeed in uniting the nation behind AUKUS.

“It’s clear now that on the left flank of the Labor Party they have great reservations about AUKUS,” he said.

He said the queries were “undermining the government’s position”.

But Hastie wouldn’t comment on whether any coalition MPs had expressed reservations about the deal.

“Our adversaries are seeking to undermine this is very deal. It’s right that we ask questions but we need to be unified around this,” he said.

A local Labor branch in the Sydney suburb of Petersham, which sits within the prime minister’s electorate, passed a resolution against AUKUS and called for Australia to withdraw from the pact with the United States and United Kingdom.

The resolution said the agreement would threaten Australian sovereignty – which the government denies – and goes against Labor’s traditional opposition to nuclear power.

“The proposed nuclear submarines are not only an obscene waste of money but will irreversibly enmesh Australia into the nuclear weapons and nuclear waste industry,” the resolution said.

The local Labor branch in Port Kembla, which is being considered as a future submarine port, also passed a resolution against the hosting of nuclear vessels in the Illawarra region on the NSW coast.

Two unions have also come out against the deal.

The maritime union’s southern NSW branch secretary Mick Cross said the basing of nuclear submarines would risk expanding shipping arising from renewable energy investment in the area.

The Electrical Trades Union has described it as a “betrayal of responsibility to Australia’s non-nuclear policy”, labelling nuclear technology as “inherently dangerous”.

Former Labor prime minister Paul Keating ignited the debate within the party when he came out against the agreement in a scathing National Press Club address last week.

Albanese last week said in an interview the caucus had been “taken through this process” and he hadn’t heard any opposition from within his party.

When the original AUKUS decision was made by the coalition government, it was put to the shadow cabinet and caucus and received the “total support of the Labor team”, he said.