• So stark is the danger of war erupting between Israel and Hezbollah that U.S. President Joe Biden last week sent one of his top aides, Amos Hochstein, to Israel and Lebanon to push for a solution. 
• Hezbollah, considered to be among the most heavily armed nonstate groups in the world, is estimated to have 10 times the military capability of Hamas.
• At least 150,000 residents of southern Lebanon and northern Israel have been evacuated from their homes and are internally displaced due to the regular cross-border fire.
• Leaders of both Israel and Hezbollah say they do not want a full-fledged war, but the risk of miscalculation is high.

The near-daily exchanges of fire along Lebanon's border with northern Israel have intensified at an alarming rate in recent weeks, spurring escalating threats between Israel and Hezbollah and forcing the U.S. to call for an urgent diplomatic solution.

An all-out war between Israel and Hezbollah — the Iranian-backed Lebanese Shiite militant and political organization, called a terrorist group by the U.S. and U.K. — would be devastating for both sides.

So stark is the danger of war erupting between Israel and Hezbollah — a far larger and more heavily armed fighting force than Hamas — that U.S. President Joe Biden last week sent one of his top aides, Amos Hochstein, to Israel and Lebanon to push for a solution. 

U.S. Defense Secretary Lloyd Austin told reporters Tuesday that "diplomacy is by far the best way to prevent more escalation," stressing that, "we are urgently seeking a diplomatic agreement that restores lasting calm to Israel's northern border and enables civilians to return safely to their homes on both sides of the Israel-Lebanon border."

Hezbollah has launched thousands of rockets into Israel in the nearly nine months since the latter began its war against Palestinian militant group Hamas in Gaza on Oct. 7. The rockets fired from Lebanon have killed 18 Israeli soldiers and 10 civilians, Israel says, while Israeli shelling has killed some 300 Hezbollah fighters in Lebanon and around 80 civilians, according to a Reuters tally.

At least 150,000 residents of southern Lebanon and northern Israel have been evacuated from their homes and are internally displaced due to the regular cross-border fire. 

"A full-fledged war between Israel and Hizbullah would be a disastrous event for the region, including both Israel and Lebanon," Victor Tricaud, a senior analyst at consulting firm Control Risks, told CNBC. 

'It only takes a single stray rocket'

The most extreme war scenario? Tricaud describes a large-scale ground invasion and aerial bombing campaign against Lebanon by Israel, heavy bombardment by Hezbollah with regular direct hits on Israeli civilian infrastructure, and potentially even the direct involvement of Iran, which would have major implications for the global economy.

A conflict of this magnitude would see national infrastructure on both sides — like water, electricity and communications — heavily damaged or destroyed, along with homes and military targets.

But for now, this remains a "comparatively distant scenario," Tricaud said, "with many escalatory steps likely to take place before the confrontation reaches such a level of intensity." 

Leaders on both sides say they do not want all-out war. Their tit-for-tat strikes over the last several months, while at times lethal, are still broadly viewed as being carefully calculated to avoid major escalation.

Lebanon, meanwhile, is in the midst of an economic and political crisis, its infrastructure wholly unprepared for a new war. A major Israeli incursion into the country would be catastrophic, particularly in Lebanon's south – a key Hezbollah stronghold – posing a serious threat to the militant organization's popularity and support there. 

"Today, each side presumes to 'teach' the other that it can inflict greater pain within the assumed rules of engagement of a limited fight," said Nimrod Novik, a fellow at the Israel Policy Forum, which is dedicated to advancing a two-state outcome to the Israeli-Palestinian conflict.

"However, it only takes a single stray rocket causing significant casualties and the adversary retaliating in kind, for things to get out of control."

Hezbollah: 10 times stronger than Hamas

Hezbollah is considered to be among the most heavily armed nonstate groups in the world. It's estimated to have 10 times the military capability of Hamas, and most previous wars between Israel and Hezbollah have ended without a clear victory for either side. 

The outcome of a 34-day war between the two adversaries in 2006, however, which saw Israeli ground troops fighting in Lebanon, was claimed as a victory by Hezbollah, and was seen as a strategic failure in Israel. The militant group is now significantly stronger and equipped with more advanced weapons than it was in 2006.  

Tricaud said Hezbollah combatants have become "increasingly battle-hardened, having taken part in the war in Syria, and will be able to leverage asymmetric warfare tactics very effectively thanks to the movement's long-standing territorial control of southern Lebanon."

He added that the toll of a full-scale war on the Israeli population "would be far higher than it was in 2006."

Retired Israel Defense Forces Col. Miri Eisin, who currently directs the International Institute for Counterterrorism in Israel, illustrated the threat of Hezbollah's weapons arsenal in the event of a full war. 

"We're talking about weaponry that we have not seen in this area," she said, describing Hezbollah's potential use of mortars, rockets, guided missiles, drone swarms, suicide drones and even ground troops to dismantle Israel's defenses. 

Simultaneously, "Israel will attack an immense amount of Hezbollah targets," Eisin said. "And Hezbollah has surface-to-air missiles that they've used very little and they have them both from Iran and from Russia."

Despite Israel's formidable air defense systems, there will still be "capabilities that will infiltrate inside Israel, which means that we will have casualties in the heart of Israel," she said.

U.S. support will be crucial for Israel in such a context; it also raises the stakes if other Iranian-backed proxy groups get involved and attack American assets.

Recent reports have cited anonymous U.S. officials as saying that the Biden administration will help Israel defend itself against Hezbollah retaliation. This could include keeping its Iron Dome air defense system stocked, providing intelligence — and possibly striking Hezbollah itself in the event of heavy attacks against Israel. CNBC has contacted the U.S. Department of Defense for comment.

Novik, from the Israel Policy Forum, still believes that the diplomatic route to de-escalation and a solution has not been exhausted.

"Indeed," he said, "the tragic irony is that the greater the risk of escalation, the more the parties are likely to make room for diplomacy. It is a typical 'too close for comfort' situation."