The United States last week fired a volley of cruise missiles at a Syrian airbase in response to an alleged chemical weapons attack that killed 87 civilians in a rebel-held town.
The White House on Monday warned that further use of chemical weapons or chlorine-laden barrel bombs could bring more US military retaliation.
"The Americans will have to pay a heavy price if they repeat their action and they must know that their actions will not go unanswered," Dehgan said during a telephone conversation with Russian counterpart Sergei Shoigu.
Dehgan accused American leaders of lying by saying they wanted to "fight terrorists".
"Instead of bombing, the Syrian army and the Syrian people are being bombed," Dehgan said, quoted in a statement on the website of his ministry.
"The resistance front will continue to fight resolutely against terrorists despite the willingness of the Americans," he added, referring to an anti-Western alliance that includes Iran, Syria and Lebanon's Hezbollah.
The statement quoted Shoigu as saying that "Russia is determined to use its political and military capabilities to bring decisive blows to terrorists".
Dehgan also spoke with his Syrian counterpart Fahd Jassem al-Freij, the defence ministry said.
The two agreed to "strengthen their cooperation to step up operations against terrorists", it said.
They also called for a commission to reveal "the truth about the Americans' false claims" regarding last week's suspected chemical attack on Khan Sheikhun.
"This kind of action (by the US) will have no effect on the determination of the resistance front to fight terrorists," they added.
Moscow said on Tuesday that Russia's foreign minister, Sergei Lavrov, will host three-way talks with his counterparts from Syria and Iran this week.