Trump struggles to pull Netanyahu back from return to all-out war: Sources

Attacks between Israel and Iran test cease-fire and U.S. influence

The latest exchange of heavy fire in the Middle East has deepened concerns within the Trump administration about its ability restrain Israel, its top ally in the region, U.S. officials told ABC News.

President Donald Trump spoke to Israeli Prime Minister Benjamin Netanyahu after Iran launched a barrage of missiles against his country on Sunday with the intention of convincing him against mounting a counterattack, according to two sources familiar with the conversation who said Trump's position somewhat softened over the course of the call.

But as Israel and Iran traded attacks, the sources said the president and his close advisers quickly became concerned about the intensity of the back-and-forth between the countries and the prospect it could lead to a return to all-out war, prompting Trump to hold another call with Netanyahu in which he more forcefully urged the prime minister to call off additional strikes.

"Israel and Iran must immediately stop 'shooting,'" Trump declared Monday morning in a post to his social media platform.

Both Israel and Iran have publicly indicated they will comply with the president's directive for now but say they could return to direct hostilities if provoked -- a scenario officials within the Trump administration see as increasingly likely due to Tehran's willingness to play a larger role in Israel's fight against its proxy Hezbollah in southern Lebanon.

In the hours before Iran launched direct attacks on Israel on Sunday -- the first since a fragile cease-fire took hold in April -- Israel carried out strikes targeting Hezbollah sites near Beirut, which Netanyahu described as retaliation for an earlier attack from the militant group. Tehran previously threatened to attack Israel if it continued its military operation against Hezbollah.

Iran's military joint command said in a statement on Monday that "if the aggressions and provocations continue, including in southern Lebanon, much more severe and decisive actions than before will follow.

In his own statement on Monday, Netanyahu insisted Iran and Hezbollah "are weaker than ever," but said "our struggle with them is not over yet."

"In the past 24 hours, Iran and Hezbollah have tried to impose a new equation on us. And this equation is intolerable and unacceptable in my opinion," he added.

While U.S. officials say the Trump administration has continued to privately urge Israel to temper its military campaign in Lebanon to make room for peace negotiations, the Israeli government has maintained the oper