The deadly exchange of fire killed two Lebanese soldiers and a journalist, as well as an Israeli officer.
The standoff was sparked when Israeli troops tried to cut down a tree on the border, prompting the Lebanese to fire on them.
Hezbollah, a Shia group which fought a bloody war with Israel in 2006, was not involved in the incident.
On Monday, Iran, which financially supports Hezbollah, offered to fund the Lebanese army.
Iran's ambassador to Lebanon met with Jean Kahwaj, the Lebanese army chief, and said Tehran was ready to "cooperate with the Lebanese army in any area that would help the military in performing its national role in defending Lebanon".
Mahmoud Ahmadinejad, the Iranian president, is expected to visit Lebanon next month and the US is concerned about the Islamic Republic's influence in the region.
Israel regards Iran as a threat and worries about its role in supporting armed groups in Lebanon.
Berman said "The incident on the Israel-Lebanon border … simply reinforces the critical need for the United States to conduct an in-depth policy review of its relationship with the Lebanese military".
"Until we know more about this incident and the nature of Hezbollah influence on the Lebanese Armed Forces … I cannot in good conscience allow the United States to continue sending weapons to Lebanon," he added.
The move came hours after Eric Cantor, a Republican representative, called for the funding to be held, warning that the lines between the Shia movement and Lebanon's armed forces had become "blurred".
"The days of ignoring the Lebanese Armed forces' provocations against Israel and protection of Hezbollah in southern Lebanon are over," said Cantor, the number two Republican in the House of Representatives.
"Lebanon cannot have it both ways. If it wants to align itself with Hezbollah against the forces of democracy, stability and moderation, there will be consequences," he said.
Check on Hezbollah
Cantor said the US had provided roughly $720m dollars since 2006 in military aid to build up a Lebanese fighting force that would serve as a check on the growing power of Hezbollah.
The US state department defended military assistance to Lebanon, saying it helped "regional stability as a whole".
"It allows the government of Lebanon to expand its sovereignty. We think that is in the interest of both our cointries," PJ Crowley, a state department spokesman, said.
The Lebanese army is still seen as underequipped compared to Hezbollah.
The army lost 170 troops battling fighters from Fatah al-Islam holed up in a Palestinian refugee camp in 2007.
Rami Khouri, a Beriut-based analyst, said the army needs new equipment.
"The Lebanese are willing to get arms from different sources ... as long as you make it clear to everybody that they're not buying their loyalty," he said.