Rare tensions are surfacing between Israel and President Donald Trump’s administration, after the US engaged in direct negotiations with Hamas regarding hostages in Gaza, including an American national.

An Israeli air strike killed four Palestinians in Gaza on Tuesday, the territory's civil emergency service said, as Arab mediators and the United States tried to hammer out differences between Hamas and Israel over a January 19 ceasefire agreement.

Adam Boehler suggested Hamas was willing to lay down its arms in exchange for a truce, in comments that frustrated some Israeli officials already concerned by his direct talks with the group.

Israel will send negotiators to Qatar on Monday in an effort to make progress in mediated talks on a return of more hostages by Hamas, Prime Minister Benjamin Netanyahu’s office said.