The CIA's covert targeted killing programme will come under fresh scrutiny on Wednesday, the deadline for Barack Obama's administration to respond to a lawsuit over the agency's refusal to confirm or deny its existence.

The federal lawsuit is part of a three-year battle by lawyers from the American Civil Liberties Union for details of the drone programme, one of the US government's most important security operations in the war against al-Qaida.

Under a Freedom of Information Act (FOIA) request filed in 2010, ACLU seeks the legal memo underlying the killing programme, the basis for drone strikes that have killed American citizens and the process by which individuals are placed on a kill list.

The administration has until Wednesday to produce papers in the suit, filed in New York, to either hand over the requested documents or to explain why they are being held. ACLU hopes it will be the first formal acknowledgment of the programme. If so the CIA would then have to respond to ACLU's FOIA request.

US drone strikes have been credited by the administration with having badly damaged al-Qaida in places like Pakistan and Yemen, but are widely criticised by rights groups over civilian killings and the secrecy that makes it impossible to determine casualty figures and whether they are military or civilians.

Over recent months government officials including Eric Holder, the attorney general, and even Obama himself have spoken publicly about drone strikes.

The US justice department has launched an investigation into the leaks.

News coverage has included a lengthy New York Times article in May that detailed Obama's role in how the "kill list" is drawn up and signed off.

But in court government lawyers continue to claim that no official has ever formally acknowledged the drones and that there might not even be a drone programme. Such was the response to a recent related ACLU lawsuit in Washington DC.

Steven Aftergood, director of the Federation of American Scientists' project on government secrecy, said the administration's current position was untenable. "Right now the government's position is a legal fiction. In other words it has taken a position that no one finds credible. It is hard to say how it can be sustained."

The CIA's stance on the issue is based on a 35-year-old judicial doctrine called Glomar, which allows government agencies to respond to requests under FOIA by refusing to confirm or deny that the records exist. It was named after a now-famous ship called the Hughes Glomar Explorer, which the CIA used in the early 1970s to salvage a sunken Soviet submarine. When the LA Times exposed the operation the agency attempted to suppress related FOIA requests, arguing that there were circumstances in which it was impossible for them even to acknowledge the existence of records without revealing facts that the government had a right to withhold.

Aftergood said the Glomar doctrine was no longer appropriate. "That was a unique, unprecedented and one-time effort," he said. "It was not a recurring programme that expands over many years and I think that's a clue to why the current position is unsustainable. The CIA did not fly one drone over one target one time, but repeatedly over years. For that reason alone the Glomar claim is inappropriate and the position untenable."

There are a number of different positions the government could take on Wednesday. It could revoke the invocation of Glomar and say, yes there is a drone programme, but then say that everything about it is classified. It could revoke Glomar and release something but not everything. Or it could continue to invoke Glomar and release nothing. It could also revoke Glomar and release everything ACLU has requested, but no one thinks this is likely.

If it continued to invoke Glomar the court may either yield to the government's position or "because of the public debate it may say 'This is ridiculous' and reject the Glomar claim and say you have to process the claim under FOIA", Aftergood said.

Lawyers at ACLU believe the government is ready to move on the issue. They point to a legal letter to the judge requesting an extension in the case. It states the request comes from Holder himself and that "given the significance of the matters presented in this case, the government's position is being deliberated at the highest level of the executive branch".

"There's only one issue" said Jameel Jaffer, the director of ACLU's Centre for Democracy. "There's nothing to discuss at a higher level except whether to acknowledge a programme they've already discussed many times."

Jaffer admits he has no idea what might happen. "They may not release anything at all, they might continue to say it's a secret. It's possible but it's absurd. On the one hand there's extraordinary public interest in the drone programme. On the other hand they recently filed a legal brief claiming it's too secret even to acknowledge. It surprised me that they were willing to say that to the appeals court in DC.

"Everyone recognised now that the programme will be an important aspect of President Obama's legacy. He ought to be thinking about this not in terms of short-term political considerations but in terms of how the programme will be viewed by history."

In the past secrecy over the drone programme had been due to diplomacy – for instance, to admit to foreign governments that military action in sovereign territory was taking place would be "awkward or worse", Aftergood said. But now the secret is out and "everyone believes it to be true".

He was sceptical there would be any release of information but said he would like to see the CIA's drone programme moved out of the category of covert action. "I would like to see them put everything on the table. To say 'What we're doing is part of the war on al-Qaida, that has been authorised as part of the authorisation of military force.' The programme ought to be normalised and disclosed and debated.

"To pretend that it doesn't exist seems like an act of bad faith. It's an attempt to forestall a controversy that is taking place anyway. The CIA has been hiding behind a pretence of secrecy. It should drop the pretence."