Lord Justice Leveson defended his inquiry into media standards today and said he “was not in any way” seeking to challenge the right of Parliament to examine any of the issues his inquiry is covering.
After repeated criticism that the work of MPs is being blocked because of the inquiry into press standards, he insisted it was for Parliament to decide "how far it goes".
It comes after Commons Speaker John Bercow said yesterday that Parliament should come first when a number of MPs raised concerns that Culture Secretary Jeremy Hunt was being shielded from full scrutiny over his links with News International because of his impending appearance before the inquiry.
Lord Justice Leveson said: "BSkyB, it is a matter for Parliament to decide how far it is appropriate to question the Secretary of State or anyone else."
He added: "It is open to the Prime Minister to take whatever steps he wishes in relation to allegations concerning one of his ministers and equally open to MPs to ask whatever questions they wish in connection with the performance of their duties."
But Lord Justice Leveson issued a stern warning to Parliament that he would drop key strands of the inquiry if it pushed for access to crucial documents first.
He said he expected to hear evidence from Fred Michel, News Corporation public affairs executive, and Adam Smith, Mr Hunt's former special adviser within the month. Mr Smith quit after emails were released by the inquiry that suggested he had given key information about the Government's plans on the controversial BSkyB deal.
But in a shot across the bows of MPs, Lord Justice Leveson warned he would drop his plan to take evidence from the two men if Parliament published or released evidence from them first.
He also insisted that the timing of the appearances of witnesses, including Mr Hunt, before his inquiry was carefully planned out.
Lord Justice Leveson insisted he was "politically neutral" but said he could see the "political significance" of recent events.
Lord Justice Leveson warned that publicity sparked by evidence or documents being discussed or released by MPs would jeopardise his inquiry.
He said: "The inquiry permits the public examination of this material in an independent, impartial manner, visible to all as it happens, after which statements will be published and whatever enquiries or investigations that either the Prime Minister or Parliament wish to engage upon will be a matter for them.
"If, however, the evidence were to have been forced into the public domain and be the subject of argument and debate in advance of the witnesses giving evidence, so that minds are potentially made up and conclusions reached, my immediate reaction would be that I would consider it unfair to subject the witnesses to further questions before this inquiry for that would inevitably require them not only to answer the concerns of the inquiry but also those of every other analyst or commentator whether from the political or press arenas.
"My attempt to maintain political neutrality would have failed. In that event, I might well conclude that it is simply not appropriate to look at this evidence at all, and I would then abandon Mr Michel and Mr Smith as witnesses and restrict the Secretary of State to other areas of his evidence."
Labour later signalled that it would hold off from tabling questions in parliament in the wake of Lord Justice Leveson's statement.
Deputy leader Harriet Harman wrote on Twitter: "Leveson to quiz Smith & Michel as well as Hunt by end May. After that we'll continue PQs if necessary."
In a statement, Ms Harman said: "The Speaker yesterday rightly asserted the rights of Parliament. Lord Justice Leveson today explained how he intended to proceed as chairman of his inquiry, and said he intended to question Fred Michel and Adam Smith, as well as Jeremy Hunt, about the BSkyB bid.
"As Shadow Secretary of State for Culture, Olympics, Media and Sport, it is my responsibility to hold the Secretary of State to account.
"Lord Justice Leveson has said today that the Leveson Inquiry will be questioning Fred Michel, Adam Smith, Jeremy Hunt and any other witnesses they might choose to call, such as Jonathan Stephens.
"So, we have today withdrawn 15 written parliamentary questions that were awaiting answer by the Secretary of State.
"I will return to these questions if necessary after the further evidence to the Leveson Inquiry."