Nadimeh, left, mother of Ali Mounzer, one of the three Lebanese soldiers who were killed at an army checkpoint, mourns his death in Riyaq village on May 28, 2013. (REUTERS)

The rebel Free Syrian Army threatened Tuesday to “chase Hezbollah to hell” if its fighters are not withdrawn from Syria, as a fresh salvo of rockets rained down on the Lebanese Shiite movement’s heartland of support, further drawing Lebanon into Syria’s bloody civil war.

The shooting of three Lebanese soldiers Tuesday at a checkpoint near the Syrian border — decried by Lebanese President Michel Suleiman as an attempt to “stir up strife” — underscored the worsening instability in the fragile nation.

Politically polarized, Lebanon has attempted to pursue a policy of “disassociation” with the two-year-old uprising against President Bashar al-Assad. But that facade is now in tatters: Ministers with alliances to Damascus have traveled to meet Assad, while others have publicly supported the opposition.

When Hezbollah, which wields significant control over the country’s weak caretaker government, openly admitted sending fighters to Syria on Saturday and pledged to back Assad to the hilt, it marked the end of any pretense of neutrality.

Hezbollah’s support of Assad has drawn a fierce backlash from groups that oppose the Syrian government on both sides of the border. In apparent retaliation, rockets have been fired on Hezbollah targets in Lebanon with increasing frequency in recent days. At least seven struck the largely Shiite area of Hermel in the Bekaa Valley on Tuesday, injuring several people. Four rockets were fired Monday in the same area, killing a 17-year-old girl.

Hezbollah has used the area as a base to fire missiles at rebel targets in Syria, and, while there were no immediate claims of responsibility for the latest rockets, the opposition Free Syrian Army has admitted similar rocket attacks on the area in the past.

On Sunday, Beirut was hit by rocket fire for the first time since the beginning of the Syrian conflict, as two rockets slammed into the southern suburbs near Hezbollah’s headquarters. That attack came just hours after Hezbollah’s leader, Hasan Nasrallah, said he would back Assad “to the end.”

On Tuesday, Gen. Salim Idriss, chief of staff of the Syrian rebels’ Supreme Military Council, set a 24-hour deadline for Hezbollah to withdraw militants backing Assad, warning in an interview with al-Arabiya television that the rebels would take “all measures” if it does not.

The soldiers killed Tuesday were gunned down on the outskirts of the border town of Aarsal, home to thousands of Syrian refugees and a hotbed of support for the Syrian opposition. Aarsal is a transit point for smuggling fighters and supplies to the rebels fighting inside Syria, and the Lebanese army’s effort to tighten border control in the area has caused friction with residents, as well as refugees, who ally themselves with the rebels.

It was not clear who was responsible for Tuesday’s shooting. The gunmen drove a black vehicle into the barren border mountains that divide Syria and Lebanon, the Lebanese army said, adding that a hunt for the perpetrators was underway.

The army is seen by many in Lebanon as the glue that prevents the country from slipping into sectarian war. But the military increasingly finds itself caught in the crossfire between opposing armed groups, or even a target for attack.

At least two Lebanese soldiers were killed in the northern city of Tripoli in recent violence between groups supporting and opposing the Syrian government. The violence has claimed nearly 30 lives over the past 10 days.

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Suleiman called the attack on the soldiers “part of a chain of terrorist acts,” in comments carried by the National News Agency.

Former prime minister Saad Hariri, leader of the Sunni Future Movement, denounced the killings as a “heinous crime” and warned in a statement that they were “an indicator of the upcoming dangers that will target national peace.”

The threat that the Syrian conflict could turn into a wider regional struggle between Sunni and Shiite Muslims, enveloping Syria’s neighbors, has added urgency to diplomatic efforts to bring an end to the conflict.

However, a Syrian Opposition Coalition meeting in Istanbul has descended into chaos, exposing deep divisions. The conclave, scheduled for three days, was intended to expand the organization to make it more representative, decide whether to attend planned peace talks and choose a new leader. The meeting now will last at least a week, Khalid Saleh, a spokesman for the coalition, said by telephone from Istanbul.

By its sixth day of fractious talks Tuesday, little had been achieved. Western nations pushing for a 22-member liberal bloc to be accepted into the coalition have been left disappointed, with just eight new members added. A video posted online, which delegates confirmed, showed a French representative berating coalition members and gave an insight into the discord.

“There was an agreement for 22; you end up with eight, there is a problem,” the French official said.

Saleh said there will be no further discussion on expansion, while a decision on whether to attend peace talks in Geneva will be delayed until a newly appointed committee has had time to “study” the issue. A vote for a new leader is still planned, he said.

Ahmed Ramadan contributed to this report from Beirut.