Netanyahu's long-awaited phone call is the first Israeli response to Clinton's sharp criticism last week over an announced expansion of Jewish settlements in the West Bank.
The move comes as George Mitchell, the US special envoy to the Middle East, prepares to return to the region for new talks with Israeli and Palestinian leaders.
Reporting from Jerusalem Al Jazeera's Jacky Rowland said that the measures could include the release of Palestinian prisoners, the removal of West Bank checkpoints and a possible delay in settlement construction works.
Our correspondent said the US administration did not want to pick a fight with Tel Aviv and is hoping that the Israelis will provide them a way out of what had become a damaging row between the two close allies.
'Progress toward peace'
US officials did not reveal details of the conversation between Netanyahu and Clinton, except to confirm Mitchell's trip and that the two leaders had agreed to meet in Washington next week.
Al Jazeera's Patty Culhane reports on Israel's move to ease tensions with its closest ally
"They discussed specific actions that might be taken to improve the atmosphere for progress toward peace," PJ Crowley, a US state department spokesman who was with Clinton in Moscow, said in a statement.
Crowley said US officials will review Netanyahu's response and "continue our discussions with both sides to keep proximity talks moving forward".
A statement from Netanyahu's office said Clinton had told him that Mitchell would arrive in Israel on Sunday for new talks on peace moves.
Nir Chefetz, a Netanyahu spokesman, said the Israeli prime minister clarified Israeli policy and suggested "mutual confidence-building measures" that both Israel and the Palestinian Authority could take in the West Bank.
Netanyahu will be in Washington next week for the annual gathering of the powerful pro-Israel lobby, the American Israel Public Affairs Committee (AIPAC), with Clinton also scheduled to speak there on Monday.
Relations between Israel and the United States have been unusually tense this week after Israel announced a plan to build 1,600 housing units near occupied East Jerusalem during a visit by Joe Biden, the US vice-president.
|Hillary Clinton had sharply criticised Israel's settlement announcement [Reuters]
Last week Clinton denounced the Israeli housing move as an insult and a repudiation of US efforts to get Israel to halt construction of additional Jewish settlements.
"Our goals remain the same," she said on Thursday in Moscow.
"It is to re-launch negotiations between the Israelis and the Palestinians on a path that will lead to a two-state solution. Nothing has happened that in any way affects our commitment to pursuing that.''
Israel sees Jerusalem as its capital, though this is not recognised internationally.
The Palestinians want East Jerusalem, captured by Israel in 1967, to be capital of a future state.
The Quartet of Middle East peace mediators were to meet in Moscow on Friday about ways to resume the negotiations, stalled since December 2008.