Magyar also told parliament that his government would launch broad economic, political and legal measures to rid Hungary of corruption, including the creation of a National Asset Protection and Recovery Office.
During a live-streamed address to parliament in Budapest on Monday, Magyar said: "With the operation 'Cleansing Fire' we will free our country from the captivity of the political and economic mafia that has ruled for the past 16 years."
Magyar's conservative Tisza party won the April 12 parliamentary elections with a two-thirds majority, ousting long-serving prime minister Viktor Orban and his populist nationalist Fidesz party.
Magyar's proposed constitutional amendments are designed to allow senior officials still appointed by Orban to be removed from their posts, including President Tamas Sulyok, Constitutional Court president Peter Polt and Supreme Court head Andras Varga.
These figures are widely regarded by Magyar's supporters as loyal to the former administration, which he has referred to as "Orban's puppets."
Sulyok has said he had no political agenda and merely provided necessary checks and balances.
The president is to be dismissed by a constitutional amendment based on Tisza's two-thirds majority in parliament.
Legal changes will set the age limit at 70 years for judges at the Constitutional Court, which can block some legislation.
Orban ally Polt would then have to retire as head judge.
With its parliamentary majority, Tisza also has the power to amend the constitution and appoint successors following any removals from office.
Magyar said a country-wide consultation process on a new constitution would begin in September, culminating in a referendum.
with DPA
