The colonel's comments to the Lebanon-based Al-Mayadeen TV came as Lebanese artillery and aircraft pounded IS positions on the other side of the border as part of Lebanon's own offensive against the extremists.
Lebanese and Syrian military officials denied reports about negotiations to allow IS fighters in the border areas to leave and head to Syria's eastern province of Deir el-Zour near the border with Iraq.
The Lebanese army command said the fourth phase of the offensive that began on Saturday should eventually evict all IS fighters from the border region.
The Syrian army and its ally, the Lebanese Hezbollah group, launched an operation simultaneously with the Lebanese to clear IS from the Syrian side of the border in the western Qalamoun mountain range. Hezbollah has been fighting in Syria alongside President Bashar Assad's forces since 2013.
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Elsewhere in the fight against IS, Syrian troops and their allies besieged a large area controlled by IS in central Syria today.
The government-controlled Syrian Central Military Media and the opposition's Britain-based Syrian Observatory for Human Rights said Syrian troops have now surrounded an area of 2,000 square kilometers (772 square miles) in the Syrian desert, widely referred to as Badia.
This adds to another area in central Syria, similar in size, which came under government siege earlier this month. Syrian troops have captured wide areas from IS in northern and central Syria over the past months, under the cover of Russian airstrikes.