Patriarch Rai called upon the Lebanese authorities to take "immediate and wise measures to halt the conflict and reunite the people of Tripoli."
"We pray also for the people of Tripoli and peace in the city," he said, expressing sympathy for the victims and their families.
He stressed that Lebanon is greatly influenced by what is happening in the region.
The patriarch's remarks follow a late-May statement from the Maronite Council of Bishops, which warned against attempts to drag the country toward "a new war through fueling sectarian tensions."
The bishops urged officials to shield the army from political tensions that would harm its credibility and warned against divisions within the country's military and security institutions.
"Harming its unity will lead Lebanon toward a dangerous path," cautioned the bishops.
They emphasized that "the government's institutions are the sole (authorities that can) resolve conflicts."
They said Lebanon's citizens are entitled to take part in determining the future of their country without placing one faction's interests above the other.
Lebanon has been plagued by political infighting, even among its Maronite Catholic political parties. Lebanon's president has called for the country's political factions to resume national dialogue sessions, setting June 11 as a meeting date.
"Officials must comply with President Michel Suleiman's call to resume the national dialogue without preconditions," the bishops said.
Following a June 4 meeting with the patriarch at Bkerke, Lebanese Prime Minister Najib Miqati said the tensions in Tripoli "date back several decades, and I call on everyone to practice self-restraint."
He maintained that his government is "preserving stability," saying that through "unity and awareness" Lebanon can prevent a spillover of the Syrian crisis into their country.
Lebanon's population of nearly 4 million comprises 18 different religions, 12 of which are Christian. While there has been no official census in decades, Christians are thought to represent about 33 percent of the population.
However, due to instability in the country and the region, Christians have been emigrating in increasing numbers.