Jerusalem (CNN) When US President Donald Trump meets with Israeli Prime Minister Benjamin Netanyahu on Monday ahead of the United Nations General Assembly, the conversation itself will be private, but Netanyahu has made it very clear what he wants to discuss: Iran.

Netanyahu's first dire warning about Iran came more than two decades ago. In 1996, Netanyahu, then in his first term as Prime Minister, delivered his maiden speech before Congress. In it, he warned that Iran "has wed a cruel despotism to a fanatic militancy. If this regime, or its despotic neighbor Iraq, were to acquire nuclear weapons, this could presage catastrophic consequences, not only for my country, and not only for the Middle East, but for all mankind."

In the intervening years, his language has barely changed.

In 2011, again speaking before Congress, Netanyahu said, "The tyranny in Tehran brutalizes its own people." In 2015 -- his most recent speech before Congress in which he lobbied against the Iran nuclear accord -- the Israeli Prime Minister said, "Iran's founding document pledges death, tyranny, and the pursuit of jihad."

What has changed is Netanyahu's singular focus on Iran. He mentioned it only once in 1996. In 2011, he said it 12 times. In 2015, he said "Iran" a staggering 107 times in his speech.

Once the most vocal critic of the Iran nuclear deal, officially called the Joint Comprehensive Plan of Action (JCPOA), Netanyahu went largely quiet after the signing of the accord in July 2015, realizing he could do little to change it, especially as relations deteriorated between Netanyahu and former President Barack Obama.

In Trump, Netanyahu sees a new window of opportunity.

Trump has blasted the Iran deal since his days on the campaign trail, calling it "the worst deal ever" and vowing to "rip it up." Since taking office, his tone has softened, but only slightly.

Trump has still voiced strong criticism, leaving open the possibility that the United States will leave the deal, despite the International Atomic Energy Agency finding at the end of August that Iran was complying with the terms of the accord. Earlier this month, US Ambassador to the UN Nikki Haley laid out a case for the US to abandon the deal, saying Iran's technical compliance wasn't enough.

Netanyahu has urged Trump to do so, saying in an exclusive interview with CNN this week, "This agreement should be changed. It should be changed so that the removal of restrictions on Iran's nuclear program should be not a matter of [a] change [in] the calendar, but a change in Iran's aggressive behavior. They must stop their aggression. They must stop their terror in the Middle East and everywhere else."

Israel's concern about the nuclear deal isn't the only Iran issue Trump and Netanyahu will discuss. In fact, it may not even be the primary one, since even Netanyahu acknowledges that the current accord will keep Tehran from developing a nuclear weapon within the next decade.

Hezbollah's evolution

Hezbollah's secretary general Hasan Nasrallah delivers a televised speech to Lebanese supporters in August.

Across Israel's northern border among the rolling hills of southern Lebanon, Iranian-proxy Hezbollah has built a stronghold. A few feet away from the border, near the Israeli town of Malkiya, a Hezbollah flag marks the territory. On a nearby hill, another flag waves in the breeze, near a UN outpost.

Since Israel and Lebanon fought a month-long war in the summer of 2006, this border has been Israel's quietest, despite the war ending with no clear winner or loser. But the tranquility masks a simple truth -- the border is perpetually tense.

Last week, Israel ran its biggest military exercise in twenty years along the northern border, including its army, air force, and navy, simulating a conflict with Hezbollah. And for years, Hezbollah's arsenal has been growing — now with 100,000 short range rockets and several thousand more missiles in its cache, according to state-run Iranian news agency Tasnim and Israeli officials. Once a guerilla militia, Hezbollah is now an experienced army, learning from the conflict in Syria, where it has fought alongside the Syrian regime.

"In the last five years, there is a huge, dramatic change in the tactical, but also operational capabilities of this organization as a fighting organization. You find yourself with an organization that is working with military formations - battalions, brigades - that has a command and control structure that has dramatically changed," General (Res.) Eli Ben-Meir, the former Chief Intelligence Officer of Israel's military said.

Even so, over the last decade, Israel and Hezbollah have preferred to shoot rhetoric back and forth across the border instead of live fire. But increasingly it is Iran's deployment of Hezbollah in neighboring Syria that is alarming Israel.

Having seen Iran establish a foothold in Iraq, Israel is desperate to prevent Iran from setting up another in Syria.

Last year, Netanyahu acknowledged that Israel struck Syria dozens of times to prevent advanced weaponry from reaching Hezbollah, also saying Israel would work to prevent Iran from digging in along Israel's borders.

The Russia connection

To push back against Iran's growing influence, Israel has turned not to the US, but to Russia. Netanyahu has made regular trips to Russia to meet with President Vladimir Putin ever since Russian forces moved into Syria in 2015, touting the Israeli and Russian military coordination over Syria. But Israeli politicians are acutely aware that Russia's primary concern in the region is its own interests, not Israel's security.

This is where Israel feels the lack of US presence in the region most sharply -- starting in the Obama administration. Despite Trump's tough talk on the Iran nuclear deal and the possibility of harsher measures against Iran, he now presides over what many Israelis regard as the absence of the US in the Syria conflict. In multiple conversations with Israeli politicians, this fear is often repeated.

"The United States can prevent a permanent Iranian military presence in Syria," Minister of Intelligence and security cabinet member Israel Katz told CNN, urging the US to get more involved. "I think the lesson both in the nuclear sphere and the conventional sphere is that the US cannot ignore the fact that she is the leader of the free world and everything that comes from that."

Sebastian Gorka, who until recently served as a counter-terrorism adviser to President Trump, tried to allay Israeli fears. "Key individuals inside the National Security Council understand we are at war with Sunni Jihadis - al-Qaeda, ISIS - and they also understand that any action we take against groups like ISIS should not occur in ways that profit Iran in ways that are strategic and long-term," Gorka said in an interview with CNN, on the sidelines of a counter-terrorism conference in Herzliya.

"I hope those voices maintain their positions and their influence. Again, this is about the long game.

But without a concrete plan, Gorka's statements do little to ease Israeli fears.

Another full-blown conflict between Israel and Hezbollah would be devastating for both sides. Hezbollah has the rockets and missiles to hit deep within Israel. Israel has the firepower to level southern Lebanon.

Israel's fear is that, if there is another war, Israeli forces may have to go it alone.