Centre had named Vice Admiral Karambir Singh as the new Navy Chief last month.
A military tribunal on Thursday gave three weeks to the Defence Ministry to decide on a petition by Vice-Admiral Bimal Verma, challenging the appointment of Vice Admiral Karambir Singh as the next Navy Chief overlooking his seniority.
Vice Admiral Verma, the senior-most naval commander, on Tuesday once again moved the Armed Forces Tribunal in Delhi challenging appointment of Vice Admiral Singh to the top post after the defence ministry did not respond to his statutory complaint.
Mr Verma, commander-in-chief of the Andaman and Nicobar Command, approached the Armed Forces Tribunal (AFT) on April 8, but withdrew his petition the next day after the tribunal asked him to first explore "internal remedies".
"The AFT has directed the government to dispose of Vice Admiral Verma's petition by May 15 and fixed May 20 as the next date of hearing in the case," Mr Verma's lawyer Ankur Chhibber said.
He said though the government sought four weeks' time, the AFT granted only three weeks to it.
Vice Admiral Verma filed a statutory complaint with the Defence Ministry on April 10, challenging appointment of Vice Admiral Singh as the next navy chief, and asked it to respond within 10 days.
However, as there was no response from the ministry, he again approached the AFT on Tuesday.
Mr Verma, the senior most naval commander, is contesting appointment of his junior Vice Admiral Singh to the top post.
In his petition, Mr Verma wondered why he was overlooked for the top post despite being the senior-most in the line of command, terming as "wrongful" the government's decision to appoint Mr Singh to the post.
The government had last month named Vice Admiral Singh as the next chief of naval staff, to succeed Admiral Sunil Lanba who retires on May 30.
The government made the selection following a merit-based approach and did not go with the tradition of appointing the senior-most eligible officer to the post.
Mr Verma, senior to Mr Singh, was among the contenders for the top post.
While appointing the Army chief in 2016, the government did not follow the long-held tradition of going by seniority. Bipin Rawat was appointed Army chief superseding then Eastern Command Chief Lt Gen Praveen Bakshi and Southern Command Chief PM Hariz.
Besides Mr Verma, the other contenders for the Navy Chief post included Vice Chief of Naval Staff Vice Admiral G Ashok Kumar, FOC-in-C of Western Naval Command Vice Admiral Ajit Kumar and FOC-in-C of Southern Naval Command Vice Admiral Anil Kumar Chawla.
Mr Singh, who is at present serving as the Flag Officer Commanding in Chief (FOC-in-C) of the Eastern Naval Command in Visakhapatnam, will be the first helicopter pilot to become chief of naval staff.
Mr Verma is brother of former Navy chief Nirmal Kumar Verma.