The relationship between Donald Trump and Benjamin Netanyahu is, by their own admission, excellent.

But the longer the war in Iran lasts, the more the interests of the American president and the Israeli prime minister diverge, according to experts.

Both on a tactical level, for example on the choice of targets, and on a strategic level, namely the moment when each will be able to claim victory.

President Trump, who acknowledges "differences" with Mr. Netanyahu, expressed his disagreement Thursday with the Israeli strike targeting Iran's South Pars gas field. The Islamic Republic retaliated by attacking a refinery in Qatar, sowing discord in financial markets.

"I told him not to do that, and he won't do it again," he stated at the White House.

The two leaders maintain a close relationship, "extraordinary" even, according to Donald Trump. "Bibi," as the American president calls him, asserts that there have never been two leaders as in sync as Trump and himself.

The Israeli leader has made no fewer than six trips to Washington since the Republican's return to power, including one a few days before the start of the war that began on February 28.

Tactically, the two historical allies have operated a clear division of tasks: Israel is focusing on the Iranian leadership, having killed Ayatollah Ali Khamenei on the first day of the war and many other senior officials, while the United States is targeting military and missile facilities.

Appearing before a parliamentary committee on Thursday, the head of US intelligence services, Tulsi Gabbard, said nothing different.

"The objectives set by the president differ from those set by the Israeli government," she noted.

"The operations carried out clearly show that the Israeli government has been committed to neutralizing Iranian leaders," while the president's objectives "are to destroy Iran's ability to launch ballistic missiles, its ability to produce ballistic missiles, as well as its navy and its ability to lay mines," she said.

But while President Trump claims to have "decimated" Iran's military capabilities, Israel has said it still has "thousands of targets" to strike in Iran, and has vowed to continue targeting officials, including Iran's new Supreme Leader Mojtaba Khamenei.

- Too expensive?

This is where the two visions can collide.

"Israel and the United States share a number of common goals, but there are differences, which are likely to increase over time," said Dan Shapiro, former US ambassador to Israel under Barack Obama.

"And I think there is no doubt that Israel would want to continue this campaign and hopes that it will lead to the fall of the regime, for very understandable reasons," he told CNN.

"The Israelis are quite consistent. They do not hide that their objective is regime change," adds Yossi Mekelberg of the Chatham House think tank in London, while President Trump blows hot and cold on this issue.

"When everything is going perfectly, everyone is happy (...). If things start to go really wrong, and we know that Trump is not the sentimental type, then the accusations will fly," he told AFP.

The conflict has at least taken a step forward by massively targeting production sites, in addition to oil and gas storage and transport, hindering global supply.

Strategically, Donald Trump and Benjamin Netanyahu both mentioned regime change in Iran at the beginning of the war, but the American president seems to have since moved away from it.

This war is unpopular with the American public, including among some of Trump's voter base, and has led to higher gasoline prices for consumers and market turbulence just months before the midterm elections in November.

Trump also maintains close relations with the Arab Gulf monarchies, long-time allies of the United States, which serve as bases for American troops and are therefore targeted by Iran.

According to Brian Katulis of the Middle East Institute in Washington, "it is not inconceivable that Trump believes the cost of this war is becoming too high and is hindering his domestic policy."

But he still needs to "chart an honorable exit strategy," the expert adds.