"I hope to soon have the honor of a visit from His Holiness to my beloved Egypt," Tawadros said Friday.
Tawadros' invitation comes after a meeting of the religious leaders Friday at the Vatican. Tawadros said the meeting said had "bolstered fraternal bonds."
Francis has scheduled a second meeting with Merkel, Italy's ANSA news agency reported. The German government said Friday that the meeting is scheduled for May 18.
Merkel first met the pope during his inauguration in March.
During mass Friday, the pope said Christians are people of joy; not a superficial joy, but one that comes from "a deeper thing, a gift from God which fills us up inside."