Labour leadership candidate Andy Burnham has branded the House of Lords "a national embarrassment" and wants it to be scrapped.
The MP for Leigh posted his comments about the upper house to the social media site Twitter.
Mr Burnham proposed that a better alternative would be an "indirectly-elected Senate of regions and nations".
He said that he favoured a proportional second chamber built from votes for the House of Commons, which would make every vote count.
On the subject of reforms to the House of Lords, Downing Street has said that David Cameron is willing to consider new all-party talks to address issues.
The prime minister indicated that he is "open" to introducing term limits in the House of Lords, but has stressed he will not attempt to force through reforms.
He had come under criticism for appointing 45 new members to the Lords, including party donors, MPs and special advisers.
Among the new members are former Tory cabinet ministers William Hague and Andrew Lansley.
The appointment of new members to the House of Lords brings the total to 826.