The president praised Japan as "an inspiration to the world culturally and economically". He also said the "special relationship between Hungary and Japan" must be further strengthened.
President Sulyok personally congratulated the new pontiff on his election after attending mass in the Vatican on Sunday morning.
The prime minister wrote on his social media page: "We have a pope! There is hope!"
The president helped welcome MTA's 200th anniversary of its foundation.
The president said Central Europe, including Hungary, was "a bridge" for cooperation between East and West.
The president said that when it came to Pope Francis, he had always felt that the pope had prioritized personal relationships, and that he had emanated "great joy and great freedom".
The president said the protection of children transcended national interests, and caring for them was the most basic human inclination.
"With his presence, the president wishes to express Hungarians’ love and respect for the Holy Father," a statement said on Tuesday.
The president wrote: "He spoke in the language of the people, so that everyone may understand him. And many did. He spoke to us Hungarians several times. We think of him with gratitude."
The president said talented Hungarian youth would hopefully become renowned scientists and researchers.
The two leaders were in agreement that they shared the same views on issues concerning security, national sovereignty and national identity.
The president said that "Hungarian-Polish friendship for us is not a myth, but a reality."
March 15th marks the beginning of the 1848-49 revolution and war of independence, and was declared a public holiday in 1989.