The Conservatives pledged before the general election to replace the Human Rights Act, introduced by Labour in 1998, with a new Bill of Rights.
It follows concerns about rulings by the European Court of Human Rights and their application to the UK.
Opposition parties and a minority of Tories oppose scrapping the HRA.
Proposed legislation on a Bill of Rights and Responsibilities will not feature in the government's programme for the year ahead, announced by the Queen, either in full or draft form.
However, ministers have insisted they are committed to the plans and are consulting on the issues involved.
The Human Rights Act formally incorporated the European Convention on Human Rights, of which the UK was a founding signatory in 1950 and which came in force in 1953, into UK law.
Campaigners say the Act is a guarantor of fundamental freedoms, allowing people to challenge abuse, neglect or mistreatment, and that scrapping it would amount to "populist games with hard-won freedoms".
But critics have said that European courts have strayed into areas, such as prisoners voting rights, that should be the preserve of Parliament and should be left to the British courts.
The BBC's deputy political editor James Landale said that while the Conservatives had never said the measure would feature in its first Queen's Speech, it was now effectively being put "on the backburner".
The government faced a tough fight over other legislation, he said, and the prime minister wanted to "choose his battles" - adding that No 10's view was that "we still want to do it but not now".
Employment minister Priti Patel told the BBC that the government wanted to "bring sovereignty back to British courts" and the HRA had resulted in a "great deal of friction" between the British and European courts.
But she said it was right for the government to "take time" and "implement its manifesto in the right way". "It is important that we concentrate on doing these things properly," she said.
Labour said the government had "got the jitters" after calculating it could not get the measure through the Commons, while the SNP said the issue had been "kicked into the long grass".
The government is to launch a consultation on introducing a British Bill of Rights but there will be no legislation in the Queen's Speech.