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Kerry, the former head of the Senate Foreign Relations Committee, replaced Hillary Clinton on Friday.
America's new top diplomat spoke with Israeli President Shimon Peres on Saturday, State Department spokeswoman Victoria Nuland said in a statement.
On Sunday, he also spoke with Israeli Prime Minister Benjamin Netanyahu and Palestinian president Mahmud Abbas.
Netanyahu briefed Kerry on his work forming a new Israeli government, Nuland said, while the secretary of state "underscored his personal commitment and that of President (Barack) Obama to support Israel's security and to pursue a lasting peace between Israelis and Palestinians."
With Abbas, Kerry "pledged to continue efforts with the Congress to release budget support funds for the (Palestinian Authority) and noted the positive step the Israelis had taken by releasing the tax revenues," Nuland said.
Israel said last week it had released $100 million of the tariffs and tax monies it collects on behalf of the Palestinian Authority, which were frozen last year as punishment for winning upgraded status as a non-member state at the United Nations.
But an Israeli official said it was a one-off measure to ease the financial crisis faced by the Palestinians and was not a sign that the transfers would be renewed.
Talks between the Palestinians and the Israelis have been stalled since September 2010, with the Jewish state's continued settlement construction in the occupied West Bank and East Jerusalem a chief roadblock for Abbas and his government.
Separately, Kerry also spoke with Japanese Foreign Minister Fumio Kishida and discussed North Korea's nuclear stand-off, trade and the controversial US Marine Corps Air Station Futenma on Okinawa Island.
They stressed, along with South Korean Foreign Minister Kim Sung-hwan on a separate call, "the need to ensure that (North Korea) understands that it will face significant consequences from the international community if it continues its provocative behavior."
Intelligence sources worry North Korea has completed preparations for a third nuclear test it threatened to conduct in response to tightened UN sanctions imposed for a long-range rocket launch in December.
In a call to his Turkish counterpart, Kerry thanked Ahmet Davutoglu for his "excellent bilateral cooperation" after Friday's suicide bomb attack on the US embassy in Ankara that left a Turkish guard dead and three others wounded, Nuland said.
Both leaders "underscored the vital importance of the strongest possible counterterrorism cooperation" and exchanged views on Syria and the Middle East, she added.
Kerry also called his Canadian counterpart, and agreed that their two countries would "work closely together" on support for Arab Spring countries, maintaining international unity on Iran and the situations in Syria and in Mali, according to the spokeswoman.
The pair agreed to stay in touch about construction of the proposed $7 billion Canada-to-Texas Keystone XL oil pipeline, which many activists fear could damage the environment.
In his call with Mexico's Foreign Secretary Jose Antonio Meade Kuribrena, Kerry expressed condolences for the the mysterious blast at the headquarters of Mexico's state-owned oil firm Pemex that killed 33 people and injured 121 on Thursday.