Culture Secretary Maria Miller will meet the newspaper industry's most powerful editors next week to push for urgent action in setting up a new press watchdog.
The Tory minister will warn Fleet Street it must not drag its feet when it comes to acting on Lord Justice Leveson's calls for it to devise an independent regulatory body.
Lord Hunt of Wirral, chairman of the Press Complaints Commission, who will also attend, told The Times he wanted a speedy industry resolution to help persuade the public and MPs laws were not needed to underpin the new regulator.
"There's an awful lot we can agree on and I have suggested to the industry (that we) all read the report, digest it and seek out the common ground and unite with one voice," he said.
Ms Miller's warning will come the day before editors on the Code of Practice Committee, chaired by Daily Mail editor Paul Dacre, meet to decide how to tackle the Leveson recommendations.
Mr Dacre said: "Lord Justice Leveson has set us a number of challenges: our task is to address them as urgently as possible."
It comes as reports emerged that Foreign Secretary William Hague warned Cabinet colleagues earlier this week that a "Leveson law" would undermine the UK's ability to address freedom of speech issues globally, particularly on cases like the jailing of punk band Pussy Riot in Russia.
A government source told The Daily Telegraph: "It was a very serious presentation. He warned that Britain demonstrating that we have a free press is part of our ability to say we believe in democracy."
But David Cameron is under intense pressure to drop his opposition to a law backing up the new watchdog the press have been tasked with devising.
The Prime Minister faced a backlash from victims of media intrusion over his resistance to legislation and best-selling novelist JK Rowling, who gave evidence to the inquiry, waded into the row saying she was "alarmed and dismayed" at the way he had responded.