Tony Blair has dropped plans to get rid the remaining hereditary peers before the next general election.
There are 92 remaining hereditary peers in the Lords
Lord Chancellor Lord Falconer said the plans were unlikely to succeed and so there was no point spending more time in Parliament on the issue.
Most hereditary peers lost their voting rights in the House of Lords in 1999, but 92 were allowed to stay on.
Government critics say the final shape of the Lords should be decided before the last hereditaries are removed.
The government has grown increasingly frustrated in recent months with its inability to get legislation through the upper house.
Lord Falconer said peers' recent decision to send plans for a new supreme court to a special select committee made it clear they would not pass the House of Lords Reform Bill.
"It became absolutely clear the bill wouldn't get through the Lords," he told BBC Radio 4's Today programme.
"The Lords have indicated clearly they are going to resist. The leader of the Conservative party said he would fight every part of our legislative programme.
"We have got to focus on the things that really matter when there is no more than about two years to go before an election, at the latest.
"The critical thing is to focus on what our priorities are."
Jack Cunningham, chairman of the joint committee on Lords reform, said it had been "clear for some time that things were going wrong".
He said the government climbdown proved peers were "robust and resilient and would resist change", but, he added, it was an "opportunity lost".
There was a "lot of party politicking going on", with the Tories on the one hand trying to save the law lords while apparently backing an all-elected second chamber.
Liberal Democrat spokesman Lord Goodhart labelled the move a "constitutional disgrace".
"The problem in this country is that the House of Lords is not strong enough because it is unable to check a government that has a large majority in the House of Commons from abusing its position," he said.
But Conservative constitutional affairs spokesman Alan Duncan said a genuine pause would be welcome.
"It's probably good for the government because they were getting themselves into a dreadful mess and I think they had become rather perturbed on learning just how complicated these reforms always become," he said.
MPs and peers failed to agree on seven options for Lords reform ranging from a fully appointed second chamber to an all elected one.
But ministers had announced plans in last autumn's Queen's Speech to make progress against the hereditaries in what they said would be the first stage of wider reforms.
The move also hits plans to let an independent appointments' commission pick non-party peers.
Government sources say it is now likely Labour will rethink its whole strategy on Lords reform as it draws up its manifesto for the next election.
But they say publishing a draft bill is one of the options being considered as ministers try to show reform is still on their agenda.