The two leaders spoke by telephone and "agreed to continue to closely consult on a range of regional issues, including addressing the threats posed by Iran," the White House said in a statement, signaling the new administration's tougher line on Tehran.
There was no mention of Trump's suggestion to move the US embassy from Tel Aviv to Jerusalem.
Such a transfer would break with the consensus of the vast majority of the international community, which does not recognise Jerusalem as Israel's capital.
That move - long promised by presidential candidates of all stripes - could provoke a backlash in the region.
The White House on Sunday appeared to play down suggestions that a decision was imminent.
"We are at the very beginning stages of even discussing this subject," White House press secretary Sean Spicer told AFP.
Like other major powers, the US currently has its embassy in Tel Aviv.
Palestinian President Mahmud Abbas has warned that moving the embassy would deal a huge blow to hopes for Middle East peace, and the UN and EU have voiced deep concern over the proposal.
During the phone call on Sunday, Trump also stressed the need for direct talks between Palestinians and Israelis.
"The President emphasised that peace between Israel and the Palestinians can only be negotiated directly between the two parties, and that the United States will work closely with Israel to make progress towards that goal," the White House said.
Trump invites Israel's Netanyahu to US: PM's office
Trump also used the conversation to invite Netanyahu to visit the White House.
"President Trump invited Prime Minister Netanyahu to come to Washington to meet him in February," it said in a statement.
"A final date for the visit will be set in the days ahead."
The statement described the call as "very warm".
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"The two leaders discussed the nuclear deal with Iran, the peace process with the Palestinians and other issues," it said.
"The Prime Minister expressed his desire to work closely with President Trump to forge a common vision to advance peace and security in the region," it said.
Trump told reporters at the White House his call with Israel's premier was "very nice", without elaborating.
