The desert, known as the "Badiya", extends over some 90,000 square kilometres from central Syria to the borders with Iraq and Jordan to the east and southeast.
Since 2015, much of the Badiya has been held by the Islamic State jihadist group, but Syria's army has been chipping away at it for months.
Yesterday, they reached the country's eastern frontier with Iraq for the first time in two years.
"This important achievement represents a strategic shift in the fight against terrorism and a launching pad to broaden military operations in the Badiya and along the borders with Iraq," said the statement, distributed on state media.
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State news agency SANA had reported yesterday that army units set up positions northeast of the At-Tanaf garrison, currently used by the US-led coalition bombing IS to train Syrian rebels to fight the jihadists.
The US-led alliance has in recent weeks conducted three strikes against pro-regime forces it deemed to be threatening At-Tanaf.
Syria's army today accused the coalition of carrying out the bombing raids in an attempt to slow the regime's fight against IS.
"We once again warn of the dangers of repeated attacks by the so-called international coalition and its attempts to obstruct the advances of the Syrian army and its allies," the command said.
Syria's conflict erupted in March 2011 with protests against the rule of President Bashar al-Assad.