The government is to launch an initiative to get reform of the House of Lords back on the political agenda.
Ministers want the removal of the 92 hereditary peers
Lord Falconer, the Lord Chancellor, will approach the Tories and the Lib Dems to see if a consensus can be reached on its powers and structures.
In its first term the government reduced the number of hereditary peers to 92 and further changes were expected to be made in Labour's second term.
But plans were shelved after MPs could not agree the best way forward.
Lord Falconer told the BBC's Politics Show: "This initiative makes clear that the prime minister is keen to see if there is a consensus.
"If a consensus can be built, then he would support it.
"I don't know what the consensus building will produce.
"But if it produced a result where the primacy of the House of Commons were clear, and a way forward on composition was clear, then we would certainly not stand in the way, indeed we would encourage reform along those lines".
He said he believed there was general support for an "elected element" to a reformed House of Lords.
BBC correspondent Sean Curran said that, while the powers and membership of the House of Lords were not high on the list of voters' concerns, reform of Parliament's second house was unfinished business for Labour ministers.
Government sources have told the BBC this is a significant step and insist there is the political desire to complete reform of the Lords.
Following last year's Queen's Speech, peers from all parties called for a consensus to be reached on such reforms.
There was no expected bill on Lords reform in the speech, but ministers made clear their commitment to the removal of the 92 hereditary peers.
In her speech, the Queen told Parliament: "My government will bring forward proposals to continue the reform of the House of Lords."
The government says it aims to make the second chamber "effective, legitimate and more representative, without challenging the primacy of the House of Commons".