Lord Justice Leveson refused to be drawn on the press regulation row, saying "I've said what I wanted to say at length last November", as he arrived at the Palace of Westminster.
Lord Justice Leveson has agreed to give evidence to the House of Commons culture, media and sport select committee, which is investigating the future of press regulation, a Judicial Office spokeswoman said today.
Lord Justice Leveson's letter responded to Conservative MP Rob Wilson, who had demanded the judge examine the relationship between Carine Patry Hoskins and David Sherborne.
Mr Wilson wrote to the Bar Standards Board requesting an investigation into the impact of the barristers' private relations on the role both played during the inquiry.
Lord Justice Leveson said it was "a matter for the Board to decide, what, if any, action to take", adding: "In the circumstances, I do not comment further."
But he unequivocally defended the role of Ms Patry Hoskins, who he said had "absolutely no input into any conclusions" reached by the inquiry.
Lord Justice Leveson has rejected claims that a previously undisclosed relationship between two of the barristers in his inquiry into press freedom threatened the legitimacy of its subsequent report.
The judge has said today in a letter that there was "simply no room" for a "breach of confidence or other conspiracy" as a result of personal relations between Carine Patry Hoskins, the inquiry's junior counsel, and barrister David Sherborne.
Lord Justice Leveson has called for international cooperation to ensure that bloggers and tweeters are not above the law when it comes to illegal and unethical standards of journalism.
In an address as part of his Australian lecture tour, he warned there was a "pernicious and false" belief that the law did not apply to the internet.
He also said there was a chance that mainstream journalists might be tempted to break the law or infringe privacy "in order to steal a march on bloggers and tweeters".
Newspapers, he warned, may even move their bases overseas to dodge UK laws in the future.
Culture Secretary Maria Miller says the cross-party talks over Lord Justice Leveson's proposals will continue on Thursday.
Lord Justice Leveson said today that it was likely that new laws will need to be developed to protect people's privacy on the internet.
"While legal norms are in many respects capable of application to the internet, it is likely that new ones and new laws will need to be developed," he told a privacy seminar in Sydney.
He said that internet gossip that "names and shames" individuals risked "permanent and disproportionate" harm being done.
There is an emerging division in the coalition over the issue of having a statutory under-pinning for a system of press regulation.
Here is what Lord Justice Leveson says on the matter:
The Liberal Democrat Deputy Leader Simon Hughes told ITV1's The Agenda that he is opposed to the statutory regulation of the press.
Lord Justice Leveson's report is published on Thursday.
The Agenda is on ITV1 at 10.35pm and at 11:35pm in Scotland.