The Israeli publication ban regarding the latest investigation of Prime Minister Ehud Olmert will be lifted this week, top legal officials estimated Wednesday. The assessment, reported by Army Radio, came a day after The New York Post published details of the investigation, including the name of the foreign national alleged to be the key witness in the probe. On Tuesday, State Attorney Moshe Lador estimated that the media ban would not be lifted until after Independence Day. Lador was speaking to reporters following a hearing at the Jerusalem District Court on a request by the state to take testimony from a key witness in the investigation before he returns to his home abroad. At the same time, the Tel Aviv Magistrate's Court rejected a request by three media outlets - Channel 10, Ha'aretz and Yediot Aharonot - to lift the ban imposed last week. In another development, Channel 10 police and legal affairs reporter Baruch Kra reported Tuesday evening that the prosecution had already decided to serve an indictment against Olmert. A Justice Ministry spokesman called the report "speculation" and referred The Jerusalem Post to a statement made earlier in the day by Lador to the effect that some media reports were "inaccurate." The spokesman added that Attorney-General Menahem Mazuz, Lador and the police investigating team had met in the evening to discuss the case. One of the issues considered was whether to reduce the gag order. The police said it was too early to do so. The participants are due to meet on Wednesday for another consultation and will again consider the question of the gag order, the spokesman said. The hearing at the Jerusalem District Court was held behind closed doors before a panel of three judges, including court president Mosia Arad and Judges Zvi Zilbertal and Moshe Sobol. The court has not yet handed down a ruling on the state's request. It is also not clear at this point whether the gag order will apply to the transcript of the discussion. Until Tuesday morning, the media was not allowed to report that a hearing would take place. In the morning, however, the court issued the following statement: "With the agreement of the state and after the respondents' attorneys left the decision to the discretion of the court, we direct that at this stage it may be published that a request has been filed to depose a foreign national. There is nothing in this to attest that an indictment has been submitted against the respondents in the request, Prime Minister Ehud Olmert and Ms. Shula Zaken. This is an investigation that began in recent days, and the request is necessary given the circumstances under discussion. "Today, the court will discuss the deposition request. A decision on the matter, including on the question of whether to apply the ban on publication to the discussion of the deposition request, will be made after it has been heard." At the hearing, Lador and Jerusalem District Attorney (Criminal Matters) Eli Abarbanel represented the state. Olmert was represented by attorneys Eli Zohar and Ro'i Blecher, while Zaken, the prime minister's long-time aide, was represented by attorney Micha Fetman. Tuesday's request for a deposition by the key witness is based on a rarely used procedure in the Criminal Procedures Law. The state wants to question the witness as if Olmert and Zaken were on trial, since it is not certain whether he would return to Israel if and when a trial actually took place. If the court approves the state's request, Olmert's and Zaken's lawyers will be allowed to cross-examine the witness according to the same principle - that is, as if this were a trial procedure. "This investigation is at a stage where any conclusion that the public would draw would be incorrect," Lador told reporters. "No assumption and no evaluation could be well-founded at this point. In the past few days, the media has published facts that are not accurate." Asked about the significance of the deposition request, Lador said it was "part of routine work procedures in these kinds of matters, even though this affair is a little different. In this case, we are investigating suspicions against a prime minister in office, and therefore it was the right thing for me to join the team of attorneys. There is no reason to draw conclusions from this that there will be an indictment." Zohar told reporters the "gag order prevents us from saying anything about today's hearing, including our position." Asked what his position on the gag order was, Zohar said, "On the one hand, it causes harm to the prime minister. On the other, our position on this matter could be interpreted as if we wanted to obstruct the investigation. Therefore, we equivocate between the two positions." Zohar also pointed out that if the court granted the state's request for a deposition, he and Zaken's lawyers would be given all the evidence compiled so far by police to prepare for the cross-examination. Zaken's lawyer, who was interviewed by Israel Radio later in the day, denied reports that the police had offered Zaken the option of becoming a state's witness against Olmert. Zaken was questioned for the fourth time in the past week, and for the fourth time refused to answer police questions. Fetman said his client had told the police she refused to discuss the latest affair until the investigation on the matter of the Tax Authority was concluded. Meanwhile, the media ban on the Olmert investigation was undermined on Tuesday after The New York Post Web site published the name of a person alleged to be the key witness in the investigation. The court-imposed gag, which applies to media outlets operating in Israel, forbids the naming of key suspects and witnesses or lines of inquiry in the investigation. The ban has already been breached by some local reporters, and police have already questioned Yediot Aharonot reporter Yuval Yoaz, who published details of the investigation last Friday without naming names. The latest revelation abroad will only add to existing pressure to have the ban lifted. Asked to respond to the New York Post report, a police spokesman said that "the Justice Ministry will decide [what to do about] the ban, and in the meantime, the investigation is continuing as normal. Right now, there is a ban, and that's what we are adhering to." In a related development, the Legal Forum for the Land of Israel called on Mazuz to order Olmert to take a two-day leave of absence during Remembrance Day and Independence Day "so as not to cause harm to these days or to the ceremonies surrounding them."