The Prime Minister is under pressure from integrity-focused crossbenchers after appearing to walk back a promise to implement the watchdog by 2023.

But Mr Albanese threw down the gauntlet on Tuesday, insisting he is "ready to vote" this month and warning any delay "won't be because of the Labor Party".

Mr Albanese pointed to comments made at the National Press Club in the final days of the election campaign, when he promised to "put forward" an anti-corruption proposal this year.

"It's a pretty explicit statement that I made three days [before the election]," he said.

"We will have legislation introduced in September this month. We're ready to vote for it in September, this month. We're ready to vote."

But Labor will be unable to bring the legislation to a vote this month if it pushes ahead with plans to have it sent to a joint parliamentary committee, a process likely to take months.

And as Mr Albanese spoke, Labor's own website continued to pledge to "legislate" the body "by the end of 2022".

After the death of Queen Elizabeth II on Friday forced this week's sitting period to be postponed, some independents have called for Mr Albanese to make his draft legislation public.

The Prime Minister insisted the proposal would be taken to Labor's caucus of MPs first.

"Let's be serious here ... [independent MP] Helen Haines in particular has had multiple of meetings with the Attorney-General about this. I have had meetings with members from across the political spectrum about this as well," he said.

"There is no delay here ... If there is any delay, it won't be because of the Labor Party. It will be because of non-Labor members of the House of Reps and of the Senate."

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ACT senator David Pocock, a key vote in the upper house, praised the government's early engagement with the crossbench, but called for its draft to be released immediately.

Senator Pocock said he believed legislating the watchdog, while providing proper scrutiny via a parliamentary committee, was possible.

"We have to get this done and we have to get it right," he said.

"I'm not interested in delaying or standing in the way but I do want to make sure the commission has real power and integrity."

Labor's website had initially promised it would "establish a powerful, transparent and independent National Anti-Corruption Commission".

But it was altered before election day to promise the body would be "legislated" this year, a promise which remained live on Tuesday.

In April, Mr Albanese also released a statement alongside Attorney-General Mark Dreyfus explicitly promising to "legislate" the body this year.

The so-called 'teal independents', who ran on an anti-corruption commission in May, have warned Mr Albanese walking back the pledge would set a "bad precedent".