Due to give a major address on Sunday, Mr Netanyahu spoke to Mr Obama by telephone on Monday, in a conversation described by his office as positive.
He began talks with Mr Mitchell on Tuesday after the US envoy had meetings with Israeli President Shimon Peres, Defence Minister Ehud Barak and Foreign Minister Avigdor Lieberman.
President Obama seems to hope he can achieve a historic Middle East settlement within his first term and this ambitious goal puts him on a collision course with Mr Netanyahu's government, BBC Middle East correspondent Paul Wood reports from Jerusalem.
Meetings are planned with Palestinian Authority President Mahmoud Abbas and Prime Minister Salam Fayyad on Wednesday.
Mr Mitchell will then head to Lebanon before visiting Syria on Friday and Saturday as part of increased diplomatic engagement by the Obama government with Damascus.
'Close allies and friends'
Meeting Mr Peres, the US envoy stressed the bond between America and Israel.
The US Middle East envoy meets Israel's foreign minister
"Let me be clear," he said. "These are not disagreements among adversaries. The United States and Israel are and will remain close allies and friends."
But he also reaffirmed Washington's commitment to the establishment of a Palestinian state "side by side in peace and security with the Jewish state of Israel".
Mr Peres, whose post is largely ceremonial, said it was time "to take the bull by the horns" and pursue "a state for us and state for the Palestinians".
Few details of Mr Mitchell's talks with Mr Barak were given but the Israeli defence minister's office said they had discussed the question of settlement construction.
Speaking before his meeting with the US envoy, Foreign Minister Lieberman told a parliamentary committee that he welcomed US efforts to promote peace.
"We definitely give our blessing to the American approach as a regional one, and to the attempt to reach an agreement not only with the Palestinians, but to reach a regional balance where everyone understands that there is a need to co-operate, [at least] with the constructive powers in the area," he said.
He also warned once again of the danger of Iran developing nuclear weapons: "If - God forbid - Iran obtains a nuclear military capability, the entire region, with all that this entails, will enter into a crazy nuclear arms race, with all the repercussions that need not be said."
Mr Netanyahu has yet to publicly commit himself to a two-state solution.
Some see this as a negotiating ploy, but Mr Netanyahu speaks privately of allowing Palestinians self-rule while giving them something less than full statehood, our correspondent says.
Under Mr Netanyahu's vision of an economic peace, for instance, the Palestinians would not control either their borders or their airspace.
The immediate clash, however, will come over the issue of Jewish settlements built on land occupied by Israel in the 1967 war, our correspondent says.
Mr Obama has said more clearly than any US president for a long time that settlement building must stop, while Mr Netanyahu is sticking to the established Israeli formula that there should be "natural growth" in existing settlements.
The US remains committed to maintaining Israel's security - just not to defending its gains since 1967, our correspondent says.
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