Plans to introduce closed inquests with evidence heard in private have been dropped from the government's "secret justice" bill to be published on Tuesday following a dispute between David Cameron and Nick Clegg.

Government officials heralded the move as the main concession in one of the most controversial pieces of legislation contained in the Queen's speech. It follows a well-publicised row behind the scenes that delayed publication of the bill for almost a week.

Liberal Democrats are claiming credit for ensuring that inquests will not be subjected to so-called "closed material procedures", which would mean that any information held by the security and intelligence agencies could be heard only in secret.

The advantage of the concession for the prime minister is that his deputy and his Liberal Democrat colleagues in the coalition government will be able to argue they have scored a victory.

However, the main purpose of the bill will remain – evidence and claims made by MI5, MI6 and GCHQ would be presented to the court but would not be disclosed to individuals seeking damages or making complaints. As a result, they would not be challenge the agencies. Instead, their interests will be presented by vetted "special advocates".

Judges will decide whether to agree to a minister's request that evidence should be heard only in secret on grounds of national security.

The model for extending secret hearings into the civil courts will be based on the process already in use in the special immigration appeals commission (Siac), the body which has been hearing Abu Qatada's bail application this week.

Opponents of closed material procedures say evidence that cannot be tested properly in court – the claimant cannot hear accusations being made – is not reliable. Many of the special advocates themselves objected to the draft legislation.

The bill will allow ministers to claim secrecy is needed on national security grounds for swaths of information, not only material in the hands of the security and intelligence agencies, according to reports of its contents circulating on Monday.

It will, for example, forbid evidence being heard from witnesses from a foreign intelligence agency with relevant knowledge of the case but who are not party to it.

Whitehall officials said the phrase "public interest" used in the green paper had been removed and replaced in the bill by "national security". Officials say this is a much narrower test. However, they admit the term cannot easily be defined.

Dominic Grieve, the attorney general, told Liberty's annual general meeting on Saturday that the bill filled him with a "considerable amount of distaste" but it would apply only to a "very small number of cases".

At present, Grieve said, if someone brought a claim against the state, the claim had to be struck out to avoid intelligence material from being disclosed, or the government had to settle a case out of court when the claim was "completely undeserving".

Emily Thornberry, the shadow attorney general, told the meeting that compromises needed to be made to protect citizens and said the government had yet to make out the case for "such fundamental changes".

Shami Chakrabarti, the director of the human rights group Liberty, said on Monday: "So audacious were the original proposals, it's no surprise to see slight concessions designed to sweeten the bitter and unnecessary pill."

Cori Crider, the legal director of the charity Reprieve, said: "This bill will leave [justice secretary] Ken Clarke's reputation as a civil libertarian in tatters.

"Let's all remember that this bill is coming at the very time when the UK is to be hauled into court over the rendition-to-torture of Gaddafi opponents Sami al-Saadi, Abdelhakim Belhadj and their young families. If the law goes through as drafted, the majority of evidence in those cases will never see the light of day. Surely Ken Clarke – and all of us – owe an open explanation to Khadija al-Saadi, rendered age 12."

Clarke has said the powers are needed to reassure other countries, particularly the US, that they can continue to share intelligence without fear of it being exposed in British courts. Evidence that MI5 and MI6 knew of CIA abuse of detainees emerged during a high court hearing brought by lawyers for Binyam Mohamed, the UK resident held in Guantánamo Bay.

The bill proposes that the chairman of the parliamentary intelligence security committee (ISC), currently Sir Malcolm Rifkind, should be elected by MPs, rather than being appointed by the prime minister, and that the committee can demand information from MI5, MI6 and GCHQ, but the ISC will still meet in private.

Critics of the bill have pointed out that including inquests within the new regulations would have led to relatives of servicemen and women who died in action participating in hearings where sensitive material was clearly being excluded from public sessions.

The resultant public furore might have resulted in the whole initiative being defeated. None of the civil courts to which the secret hearings are being extended involve juries, so there will be no intrusive security vetting of jurors.