So you think the cross-border talks with the Sinn Fein members could resume in a matter of weeks?
But she added "it is only a draft and we will continue to debate it as part of the cross-party talks and we will continue to seek to secure agreement".
She said her party remained willing to force a Commons vote on proposals for a new system in response to the Leveson Inquiry if cross-party talks faltered and stressed the need for progress before the end of January.
Cabinet Office minister Francis Maude has made a statement to Parliament about the affair and the prospect of restarting currently stalled cross-party talks on the future of political funding.
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The talks at Chequers will focus on cross-border security and how to engage the Taliban in effective peace talks.
Mr Cameron, Mr Clegg and Labour leader Ed Miliband met for the first in a series of cross-party talks, following the Commons debate.
BBC: Leveson: David Cameron and Nick Clegg at odds over plans
Culture Secretary Maria Miller told the BBC cross-party talks, which have so far failed to reach an agreement, would continue as it was "important to get consensus" on this.
Deputy Labour leader Harriet Harman raised a number of issues with the proposals, but said the royal charter framework would form the basis of cross-party talks scheduled for Thursday.
Abu Alawa is a village elder who talks fondly about the cross-border, inter-communal relationships before the fighting began.
Which leaves China, and the possibility of restarting cross-strait talks.
On Thursday, the prime minister called time on cross-party talks on reforms and instead published plans for a royal charter to establish a tougher press regulator.
This followed an increasing UDA rejection, particularly within that brigade, of the 1998 Good Friday Agreement, which its political allies in the Ulster Democratic Party helped to negotiate during cross-party talks.
Labour leader Ed Miliband said he would be willing to have cross-party talks to try to reach a consensus on the issue.
Southern Cross is due to meet the government and its landlords on Wednesday for crucial talks about the future of the company, which is in financial difficulty.
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He defended his decision to walk out of cross-party talks on Thursday, saying he wanted to force the issue to a head and he believed a deal could still be reached.
Following cross-party talks on Thursday night - which will resume next week - the Department for Culture, Media and Sport will begin the process of drawing up a draft bill implementing the Leveson recommendations.
The winning party has already started informal talks with the country's socialist party to form a new government, with a cross-party coalition likely to be formed by Wednesday.
Another one, a cross-party bunch from Congress called Cocopa, has been trying to bring the two sides to direct talks.
Before Thursday's talks, Egypt also reportedly eased visa requirements for Palestinians under the age of 40 seeking to cross from Gaza.
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