Supreme Court lawyer Md Yunus Ali Akond filed the petition on Thursday seeking a rule on both articles.
The law, justice and parliamentary affairs secretary, cabinet secretary, speaker and supreme court registrar were made respondents of the writ.
According to the Article 116, the president controls the judicial magistrates and its staff in consultation with the Supreme Court.
As per the Article 95, there will have specific laws regarding the appointment of the justices to the High Court. But the government has been doing the job for 45 years without making any law.
In the petition, lawyer Yunus termed the articles contradictory with concept of the independence of the judiciary.
Article 116 of 1972 constitution had empowered the Supreme Court to control the magistrates and its staff. On Monday, Chief Justice Surendra Kumar Sinha said the article is one of the main reasons behind the slow pace of the judiciary, and he advocated for reinstatement of the original article.
On the next day, Law, Justice and Parliament Affairs Minister Anisul Haq termed the chief justice's advocacy contradictory.