The public prosecutor and Tharoor's counsel contended that Swamy's application was not maintainable and it should be dismissed.
Additional Chief Metropolitan Magistrate Samar Vishal, after hearing the arguments, reserved its order on the plea saying it would be pronounced on December 10.
Swamy's plea has also sought to bring on record the Delhi Police's vigilance report on tampering of evidence in the case and claimed that it might lead to framing of additional charges.
Prosecutor Atul Shrivastava, said the case was not magistrate triable. It was triable by the sessions court so Swamy should move the application before the sessions judge at a later stage, he added.
He said the BJP leader's assistance was not required and since it was a criminal trial, the matter is between the State and the accused person and no interference by a third party was permitted.
He submitted that the purpose of a Vigilance Report is to ascertain whether the service of an officer is still required and not to determine the commission of an offence.
Senior advocate Vikas Pahwa, appearing for Tharoor, agreed with the submissions of the prosecutor that the application was not maintainable and said Swamy was "an alien to the case" and he has no locus standi to participate in the proceedings.
"It is a criminal trial. He is a stranger to the proceedings. If we start entertaining them, everybody in the country will start poking their noses in every trial,". he said.
The senior counsel added that only a victim was permitted to assist the prosecution and Swamy neither comes under the definition of a victim nor he was related to the family.
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He contended that trial court was not governed by rules of public interest litigation and even the Delhi High Court had said that Swamy had filed "Political Interest Litigation" and not a "Public Interest Litigation" and had dismissed his petition.
Rebutting the arguments, Swamy said he was not a total stranger to the case and it was he who had filed the PIL in the Supreme Court and things started moving.
He said he was asking for the vigilance report to be placed before the court and wanted that vital information may not be left out by the police.
During the hearing, Pahwa told the court that the process of scrutiny of documents annexed with the charge sheet was not complete. The court asked him and the prosecutor to complete it within three days.
After completion of the process of scrutiny of documents, the case would be committed to sessions court for further proceedings.
Pushkar was found dead in a suite of a luxury hotel in the city on the night of January 17, 2014. The couple were staying in the hotel as the official bungalow of Tharoor was being renovated at that time.
The court allowed Tharoor's plea seeking exemption from personal appearance for the day.
The court had directed Delhi Police to hand over various documents filed along with the charge sheet, including statements of witnesses, to Tharoor on a plea moved by him.
The Thiruvananthapuram MP was granted regular bail on July 7 after he appeared before the court in pursuance to the summons issued against him.
The court had on June 5 summoned Tharoor, observing there was sufficient ground to proceed against him.
He has been charged under sections 498-A (husband or his relative subjecting a woman to cruelty) and 306 (abetment of suicide) of the Indian Penal Code (IPC), but has not been arrested in the case.
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