BUDAPEST, June 1 (Reuters) - Hungarian Prime Minister Peter Magyar said on Monday, after meeting President Tamas Sulyok, that if the president ‌does not resign the government will launch legal proceedings to ‌remove him from office.

Magyar's centre-right Tisza party ousted Prime Minister Viktor Orban in a ​landslide election victory in April and pledged to remove several figures appointed by Orban to key public positions over the past 16 years.

Magyar has called on Sulyok — elected in early 2024 by lawmakers from Orban's Fidesz party — ‌to step down, accusing him ⁠of failing to represent national unity on major issues and of serving the interests of Orban and his ⁠government. Sulyok has refused to resign.

"I have told the President that if he maintains his stance and does not resign, I will inform ...the lawmakers of ​Tisza about ​our legislative proposals today and we ​will immediately start the necessary ‌procedures," Magyar said.

He said the legislative process would take about a month and would involve "removing all the puppets" who took part in "dismantling the rule of law and democracy."

Orban's Fidesz party accused Magyar of issuing an "unlawful ultimatum," and said Sulyok was fulfilling his lawful mandate which runs until 2029 ‌and could not be removed from office.

Sulyok ​previously served as head of Hungary's top ​court, a post to which ​he was also elected by Fidesz in 2016.

The presidency ‌in Hungary is largely ceremonial, but ​Sulyok can refer ​laws back to parliament for reconsideration or forward legislation to the Constitutional Court, potentially slowing or blocking Magyar’s reform agenda.

Magyar has said ​he would use ‌his party's two‑thirds parliamentary majority to amend the constitution and other ​legislation to force Sulyok from office.

(Reporting by Krisztina Than and ​Anita Komuves; Editing by Ros Russell)