Figures at the top of hackers' collective Anonymous are threatening to attack the Metropolitan police's computer systems and those controlled by the UK judicial system, warning that Tuesday will be "the biggest day in Anonymous's history".

The collective is understood to be seeking to express anger over News International's phone hacking and at the threatened extradition of WikiLeaks founder Julian Assange.

A Twitter feed purporting to belong to Sabu, a senior figure within the group and the founder of the spin-off group LulzSec, which hacked a site linked to the CIA and the UK's Serious Organised Crime Agency, promised two releases of information would be launched within a day.

"Everyone brace," he tweeted. "This will be literally explosive."

A follow-up message read: "ATTN Intelligence community: Your contractors have failed you. Tomorrow is the beginning."

The account, @anonymouSabu, has not been verified as belonging to Sabu – but it has over 7,700 followers and has been referenced by the "official" Anonymous @anon_central account on Twitter.

Sources close to the collective were unusually close-lipped about the targets of tomorrow's hack, but talk within chat channels has suggested several top-level members of Anonymous are eager to launch attacks based around Julian Assange's appeal hearing against extradition, which begins on Tuesday.

Others are also believed to have proposed targeting the Met in retaliation for alleged payments to police officers by News of the World reporters, and the general response to the phone hacking scandal.

Other speculation centres around material claimed to have been obtained last week from contractors relating to security and secrecy of "former world leaders", or plans to target a senior leaders' retreat at Bohemian Grove, California.

As is typical in the chaotic and occasionally paranoid Anonymous community, other sources close to the collective are warning some prominent members are probably engaging in "disinformation campaigns" ahead of any action.

Communication problems around the planned releases were compounded as the main chat channel used by Anonymous was offline for much of Monday, leaving even those close to senior members of the collective unable to verify rumours ahead of the release.

Rumours on Friday suggested that one Anonymous member had broken into the News International servers and taken copies of some internal emails which were being offered for sale or even ransom. However this could not be confirmed, and the Guardian has not seen any evidence that the claimed email stash is legitimate, although News International's site is understood to have been "probed" by members of Anonymous at the end of last week.

Last Wednesday, two days after the Dowler revelations, a listing of emails of NoW staff appeared on Pastebin, a favourite site for posting the results – or beginnings – of attacks against all sorts of sites by Anonymous and other hacker groups.

One source told the Guardian that News International's server had been probed for up to 30 minutes at a time last week by hackers using "proxy chaining" – a method of logging in via a number of remote computers – to disguise their identity. "Everyone thinks Interpol will get involved at some point," the source said.

The hackers' anger at the company was ignited by the revelation last week that a private detective acting for NoW had listened into voicemails on the phone of the murdered teenager Milly Dowler, which may have interfered with the police investigation to find her.

Anonymous has previously attacked PayPal and Visa over their refusal, following orders from the US government, to process donations for WikiLeaks. It has also carried out online attacks against the Church of Scientology over what is seen as suppression of information.