"The Commission is of the view that ... such a process would ensure that the most complete evidence is available to the Commission at its hearing in April 2013," the UCI Independent Commission said .
"The Commission, via the Solicitors to the Inquiry, has written to the UCI's solicitors, urging the UCI to reconsider its position."
A public procedural hearing will take place "as soon as possible", the Commission added.
On Tuesday, the World Anti-Doping Agency said it had a number of serious concerns regarding the commission's terms of reference and its ability to carry out its role without undue influence.
"In particular, WADA is concerned that the scope of the inquiry is too focused on sanctioned former cyclist Lance Armstrong ... and will therefore not fully address such a widespread and ingrained problem," said WADA.
The WADA also said the commission's June deadline would not offer enough time for a proper investigation. It also questioned the independence of the commission and was unhappy that they were not offering immunity for witnesses who come forward.
Despite its concerns, the WADA has been informed that the commission and UCI will not change the terms of reference and timetable and refuse to spend money and dedicate resources on an inquiry that has such obvious limitations.
The United States Anti-Doping Agency also had some harsh criticism for the UCI, saying it set up the inquiry to ensure a pre-determined outcome since it does not offer immunity witnesses.
Plagued by drug scandals, cycling was back in the doping spotlight this week with Armstrong reportedly ready to admit in a television interview that he had used performance-enhancing drugs during his racing career.
Cycling officials could face even bigger problems if the disgraced cyclist implicates the governing body in a widespread cover-up of his doping schemes that USADA called the "most sophisticated, professionalized and successful doping program that sport has ever seen."
Despite agreeing that Armstrong cheated his way to the top, USADA and the UCI have continued to trade thinly veiled insults.
UCI president Pat McQuaid said the USADA, whose damning investigation led to Armstrong's downfall, should have handed over its dossier on the American to a neutral investigator and that anti-doping agencies needed to share the blame because their tests failed to catch him.
USADA responded by saying the UCI's banning of Armstrong was not the end of the problem because USADA's investigation showed that doping was rife in professional cycling.
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