"If someone would like to help the army without restrictions or conditions, he is welcome," Murr said.
"But those who want to help the army on condition that it doesn't protect its territory, people and border from Israel, should keep their money - or give it to Israel instead," Murr said.
"We will confront [Israel] with the capabilities that we have."
Howard Berman, the chairman of the House Foreign Affairs Committee, said on Monday that he had suspended assistance to Lebanon on August 2 amid growing concern in Congress.
A day after the decision, fighting on the Lebanese-Israel border led to the death of two Lebanese soldiers, a Lebanese journalist and an Israeli officer. Berman, a strong supporter of Israel, said that the incident reaffirmed the concerns of Congress.
Berman had used his legislative prerogative to place a suspension on the money. It remains to be seen how long the suspension will last.
Murr said on Wednesday that the Lebanese soldier who fired at Israeli forces during the border unrest was acting on orders.
The US has given more than $720 million to Lebanon in military aid since 2006.
Lebanon's military is typically weak, for instance being virtually without an airforce, with Hezbollah's forces providing greater might against Israel in the past.
The military has previously gained assistance from Saudi Arabia, Russia and other Arab nations.
The United Arab Emirates, France, Germany, Russia and Syria are said to have provided arms to the Lebanese military in the past, according to a Center for Strategic and International Studies (CSIS) report.