Hungarian President Tamás Sulyok has agreed to step down, signing an amendment to the country's constitution which will end his presidency at midnight on Sunday.

Prime Minister Péter Magyar's Tisza party had used its majority to steamroll the law change through parliament to oust Sulyok - widely seen as a loyalist of former prime minister Viktor Orbán who lost power in April after 16 years.

Sulyok had five days to sign the amendment or risk a protracted constitutional crisis and impeachment proceedings.

He confirmed he would agree to the law change as the deadline passed on Saturday evening, but in a statement accused Magyar's government of violating the rule of law.

The amendment will remove not only Sulyok from office, but the head of the Constitutional Court Péter Polt.

It will also remove judges on the court over the age of 70, and forbids deputies who have served three terms in parliament from standing again - which applies to more than half the current Fidesz deputies.

It marks the latest and most dramatic move by the Tisza government - which saw Sulyok as a puppet of the former government - since it won a landslide victory in April. It has since swept through major constitutional changes.

Orbán had described the amendment as an act of tyranny and called for protests.

Since the April election, Orbán's party has been in free fall, reeling from the shock defeat. Orbán himself has hardly been seen in public, and refused to take his seat in parliament.