Asked whether there would be a vote in parliament this week, Fallon said: "We'd like to have a vote for military action but we've got to keep building the case."
Asked whether the government had got the votes needed to get parliamentary approval for the air strikes, Fallon told the BBC's Andrew Marr Show: "Not yet, we are working at it and we need to keep working at it."
At least 18 civilians were killed and 40 wounded in "probably Russian" air strikes on a rebel-held town in northwestern Syria on Sunday, the Syrian Observatory for Human Rights said in Beirut.
The strikes hit the Idlib province town of Ariha, which is controlled by the Army of Conquest, a rebel alliance of mainly Islamist groups, including Al-Qaeda affiliate Al-Nusra Front.
Several areas of the town were hit and rescue operations are under way with several critically wounded, the Britain-based group said.
The Army of Conquest alliance seized Ariha in May after heavy fighting with regime forces.
Russia launched a bombing campaign in Syria on September 30. It says it targets the Islamic State group and other "terrorists", but critics accuse it of targeting moderate and Islamist rebel fighters more than IS.
Russian air strikes have previously hit several Army of Conquest positions in Idlib province.