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 steamrolled 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.

He said the amendment marked a "breaking point in Hungarian constitutional democracy" and said the "core values of a free society... have been trampled underfoot for the sake of political power".

It marks the latest and most dramatic move by the Tisza government, which saw Sulyok as a puppet of the former government and had pushed for his resignation.

It has swept through major constitutional changes since winning a landslide victory in April.

The 17th amendment, passed with an overwhelming majority on Monday, ends the president's term citing "serious loss of confidence" in him.

It also removes the head of the Constitutional Court and forbids MPs who have served three terms from standing again - which applies to more than half the current deputies from Orbán's Fidesz party.

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

Since the April election, Fidesz 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.