In a televised address, the Shiite group's leader Hassan Nasrallah said rebel forces in the mountainous border area posed an unacceptable threat to Lebanon's security.
"This issue needs radical treatment. We are talking about a real aggression that exists and is present," Nasrallah said of the militants in the Qalamun area.
"The (Lebanese) state is not able to address this issue... so we will proceed with the necessary treatment and assume the responsibility and consequences."
The Qalamun region straddles the Syria-Lebanon border and was a stronghold of rebel forces until a major operation by Syrian regime troops backed by Hezbollah fighters last year.
While most of the region was recaptured, opposition militants and jihadists remain entrenched in the mountainous area that runs directly along the border, which is porous and ill-defined.
From there, jihadists have launched attacks inside Lebanon, including in August 2014, when fighters from Al-Qaeda's Syria affiliate Al-Nusra Front and the Islamic State group briefly overran the eastern Lebanese town of Arsal.
A truce ended the attack, but the groups took several dozen Lebanese security forces with them as hostages when they withdrew from the town into the surrounding mountains.
They have since executed four of them and Al-Nusra on Tuesday released a video showing some of the remaining 25 hostages warning they would pay the price of any operation in Qalamun.
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Speculation has been rife about a spring attack in Qalamun by the Hezbollah movement, which has bolstered Syrian President Bashar al-Assad against rebels in battles throughout the country.
On Monday, Islamist rebels led by Al-Nusra launched an attack against Hezbollah positions in the region, and a source close to the Al-Qaeda affiliate said "the battle in the region has begun".
But Nasrallah declined to say when the group would launch any major operation in the area.
"There are preparations, and people are seeing that and speculating about it," he said.
"But we haven't announced anything official... and even when we start, we will not issue a statement," he added.
"When we begin, the operation will speak for itself."
Hezbollah has been a key force multiplier for Assad as he has battled an uprising that began with anti-government protests in March 2011 and spiralled into a war after a regime crackdown.
But the group's involvement has worsened existing sectarian tensions in fragile Lebanon, which fought a civil war between 1975 and 1990.
The country's Shiites largely back Hezbollah and the Syrian regime, while Lebanon's Sunnis have broadly supported the Sunni-led uprising against Assad.
Earlier Tuesday, former prime minister Saad Hariri, who heads Lebanon's anti-Hezbollah bloc, warned against any operation in Qalamun, suggesting it could threaten the country's security and the lives of the security forces being held hostage.
Syria's conflict has regularly spilled into Lebanon in the form of battles along the border and bombings against Hezbollah strongholds, and the country is hosting more than 1.1 million Syrian refugees.