Ed Miliband has suggested News International should be forced to sell at least one of its newspapers.
Giving evidence to the Leveson inquiry on Tuesday, the Labour leader said the Murdoch empire's dominance of the British media fuelled its "arrogance".
He said News International had "a sense of power without responsibility" because of its 37% share of the newspaper market and its stake in BSkyB.
News International owns The Sun, The Times, The Sunday Times and the newly launched Sun on Sunday which replaced the News of the World.
"I don't believe that one person should continue to control 37%, or it's now 34% post the Sun on Sunday, 34% of the newspaper market," he said.
"My strong instinct is that's too much ... I would like to see the inquiry looking at the question of whether we should have lower limits."
"I should say we should have no worries of someone owning up to 20% of the newspaper market.
"There is then a question of between 20% to 30% where you should set a limit."
Miliband said the titles owned by the News International stable combined with its broadcast interests represented a "big concentration".
"Part of the arrogance, and I use the word advisedly, came from that," he added.
"Part of News International's sense of power without responsibility came from the fact that it controlled 37% of the newspaper market."
Miliband said he had not had good relations with newspapers owned by Rupert Murdoch's News International.
"I didn't have particularly good relations with News International newspapers before phone hacking - in particular, The Sun," he told the inquiry. "I don't think it improved post phone hacking."
But he said Labour had been too close before he became leader.
"We were too close in the sense that meant that when there were abuses by the press we didn't speak out," he said.
"It was a sense of fear I suppose in some senses about speaking out on those issues that were affecting ordinary members of the public."
He added: "We didn't speak out on those issues where there was increasing evidence about News International's behaviour."
Miliband said he had met Rupert Murdoch at a News Corporation summer party in June 2011.
"I believe I should have raised the issue of phone hacking with him," he added. "I didn't."
Miliband said his decision to call for Rebekah Brooks to resign from News International would have been seen as an "act of war" by Murdoch.