László Kövér highlighted "traditionally good relations" between the two countries, which he said had been built not only on a historical but also on an economic foundation.
"With his presence, the president wishes to express Hungarians’ love and respect for the Holy Father," a statement said on Tuesday.
The pair discussed bilateral matters and the impact that Ukraine’s planned accession to the European Union would have on Austria and Hungary.
The prime minister's social media post included a black-and-white photograph of himself with the Pope, with the caption: "We say farewell."
The day of mourning will "express the nation's gratitude for the Holy Father and the nation's grief", the deputy prime minister said.
Cardinal Erdő said Pope Francis "represented the cause of peace consistently".
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 prime minister said US President Donald Trump was re-negotiating tariffs with all countries where the US had a deficit, aiming to improve the current situation.
Gergely Gulyás said the people's opinion would determine Hungary's position on the matter.
Joyful greetings from About Hungary!
It’s tradition to eat white fish on Good Friday, while on Easter Sunday, the main meal becomes the focal point of the day.
Renowned the world over as a country steeped in tradition, Hungary celebrates Easter weekend in style with delicious food and family gatherings.
Gergely Gulyás said the draft budget was the result of "cautious planning", assuming that global economic and political changes, primarily the establishment of peace, would produce economic growth.
"It's shocking to see that some European politicians are trying to undermine the success of the peace negotiations in Ukraine," the foreign minister said.
The prime minister said Brussels would prevent Hungary's economy from developing and thereby bring Tisza to power.