"In his talks with the leaders, Prime Minister Netanyahu noted the great contribution of the late former President Shimon Peres in strengthening and deepening relations with the various countries", Netanyahu's office said in statement.
The funeral was also attended by Palestinian President Mahmoud Abbas, despite calls for a boycott by the political group Hamas. Peres' son-in-law and personal physician, Dr. Rafi Walden, said Obama had called the family overnight on Wednesday during Peres' final hours and spoke to Peres' daughter, Tzvia.
Abbas shook hands and shared a few words with Israeli Prime Minister Benjamin Netanyahu before the funeral began.
Security forces were on high alert, with roads closed and thousands of officers deployed.
President Obama hailed Peres as a man who showed the world that justice and hope are at the heart of the Zionist ideal and saw "all people as deserving of dignity and respect".
In contrast to an outpouring of grief from Western leaders, Arab leaders have remained largely silent over Peres' death.
World leaders gathered Friday morning in Jerusalem to bid farewell to one of Israel's founding fathers, Shimon Peres.
Palestinian president Mahmud Abbas alongside European Council President Donald Tusk, left, and Hungarian Prime Minister Viktor Orban, right.
An estimated 30,000 people filed past his coffin as he lay in state outside parliament in Jerusalem on Thursday.
Former US President Bill Clinton, who oversaw Peres' signing of the Oslo Accords in the 1990s, said that Peres "lived 93 years in a state of constant wonder over the unbelievable potential of all the rest of us to rise above our wounds, our resentments, our fears". He described a warm, 25-year friendship and dismissed critics who described Peres as a naive dreamer.
Netanyahu said he was a fierce political rival of Peres, Israel's leading dove, and that the two had vastly different world views.
"This award speaks to you, to your tireless work to make Israel strong, to make peace possible", Peres said in 2013.
Clinton, in his eulogy, recounted a meeting with Peres where Arab and Israeli children harmonized on a version of John Lennon's "Imagine".
"Be at peace, Shimon, dear man, exceptional leader", he said. Netanyahu and Obama chatted along the way, also speaking to Peres' family.
The ceremony was Israel's largest gathering of global dignitaries since Rabin's funeral, and was one of the most complicated logistical and security operations ever undertaken.
Prince Charles was among many world dignatories who appeared at the funeral.
Abbas' reaction stimulated anger on social media; as many criticized Abbas for not crying over the Palestinians killed by Israel.
It won Peres the Nobel Peace Prize, though it didn't deliver lasting peace in the Middle East. Upon his passing, Obama said no one did more over the years than Peres to build the alliance between the US and Israel.
Palestinians have denounced his roles in several Israeli-Arab wars since the Jewish state's founding in 1948, as well as for the Israeli presence in Palestinian territories.
He was also premier in 1996 when more than 100 civilians were killed by Israeli shellfire while sheltering at a United Nations peacekeepers' base in the Lebanese village of Qana.
Israel's Prime Minister Benjamin Netanyahu said: "Shimon lived a life of objective he soared to many heights... he was a great man of Israel he was a great man of the world".
Egypt was represented by Foreign Minister Sameh Shoukry, while Jordan also sent a minister.