Prime Minister David Cameron said there was all-party agreement around the published charter but he was "always very happy to look at other proposals".
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.
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.