The ex-president and Nobel Peace Prize victor died on Wednesday at the age of 93 after suffering a stroke.
Robby Berman, of the Halachic Organ Donor Society, commented, "One can not deny that Peres thought of other people, of Israelis in particular, and he did not let death stop him - he gave to the other even in death".
"I will always be grateful that I was able to call Shimon my friend", Obama said in statement.
An adviser to Morocco's king will attend Peres' funeral, according to Israel's foreign ministry.
Peres's body was to lie in state for 12 hours outside Israel's parliament, the Knesset, with tens of thousands of ordinary Israelis expected to pay tribute to a man who shaped so much of Israel's history.
The ceremony was held in silence, with none of the leaders speaking. It said helipads would be set up near Mount Herzl to allow easier access for visiting dignitaries and to prevent traffic jams.
Shimon Peres suffered a stroke about two weeks ago. "We share this pain together".
In this undated photo, Prime Minister Benjamin Netanyahu (L) speaks with Leader of the Zionist Union party Isaac Herzog (C) and Leader of the Joint (Arab) List, Ayman Odeh in the Knesset. "Shimon devoted his life to our nation and to the pursuit of peace", he said.
Israeli President Shimon Peres speaks to reporters outside the White House on Tuesday, May 5, 2009, after meeting with President Barack Obama in the Oval Office. "Let those of us who loved him and love his nation keep his dream alive".
Former Presidents George H.W. Bush and George W. Bush also issued statements of mourning.
In attending the funeral, Abbas wanted to "send a strong message to Israeli society that the Palestinians are for peace, and appreciate the efforts of peaceful men like Shimon Peres", the senior official said. But he never quite got his country there, even though he earned the Nobel Peace Prize in 1994 for trying. Peres, like other Israeli leaders, also allowed settlement construction to take place during his years in leadership positions.
In the Gaza Strip, a spokesman for the Hamas movement which runs the enclave said: "The Palestinian people are happy at the death of this criminal".
Peres, the Nobel Peace Prize laureate and one of Israel's founding fathers, died at a hospital outside Tel Aviv.
He was born in what was then Poland and immigrated to Israel at age 11. His other relatives stayed behind and perished in the Holocaust.
Mr Peres once said the Palestinians were Israel's "closest neighbours" and might become its "closest friends".
He was a driving force in the development of Israel's nuclear programme in the 1950s.
Dozens of leaders across the globe have been invited to the funeral of the former prime minister and president of Israel who died Wednesday. Journalist Chemi Shalev aptly quotes Friedrich Nietzsche to sum up his long, rich life of ups and downs in politics - he lost as many elections as he won: "One is fruitful only at the cost of being rich in contradictions; one remains young only on condition that the soul does not relax, does not long for peace".