Peres, 89, tweeted on Tuesday, "Your holiness, welcome to Twitter. Our relations with the Vatican are at their best and can form a basis to further peace everywhere."
Relations have taken a turn for the worse in recent days.
The Vatican last week warmly welcomed the U.N. General Assembly vote recognizing the state of Palestine—a move Israel hotly opposed and responded to by announcing plans for new settlement construction in the West Bank.
The Vatican on Tuesday led its daily newspaper L'Osservatore Romano with a highly critical news article about the planned construction.
The 85-year-old Pope isn't planning on following anyone and won't be tweeting until December 12. He joined Twitter on Monday and gained 250,000 followers within hours. He plans tweets in eight languages.
Peres, a Nobel Peace Prize laureate, has embraced social media. He visited Facebook's headquarters where creator Mark Zuckerberg helped him launch his official Facebook page in English.
In collaboration with a well-known Israeli announcer, his office released a music video, asking people to be his Facebook friend.
Additional reporting by Associated Press writer Nicole Winfield in Rome.