Video courtesy of jn1.tv
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."
The 85-year-old pope did not immediately respond. He joined Twitter on Monday and gained more than 500,000 followers the day after the Vatican unveiled his handle – @Pontifex, even though he hadn't sent a single tweet yet.
The Vatican said on Monday that Benedict would start tweeting on mostly spiritual topics from December 12. He plans tweets in eight languages – Spanish, English, Italian, Portuguese, German, Polish, Arabic and French. Other languages will be added in the future.
The pope, leader of some 1.2 billion Roman Catholics, won't be following anyone but himself, the Vatican said.
Peres, a Nobel Peace Prize laureate, has embraced social media. He visited Facebook's headquarters where creator Marc 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.
The Associated Press and Reuters contributed to this report