"This is a turning point in the crisis, both militarily in terms of the army's achievements in the war against terror, and socially in terms of national reconciliation processes and growing awareness of the truth behind the [attacks] targeting the country," he said.
Syria's army has made a series of advances in recent months, overrunning opposition bastions near the Lebanese border and in the central province of Homs.
"The state is trying to restore security and stability in the main areas that the terrorists have struck," said Assad, adding "we will go after their positions and sleeper cells later".
But there is still no political solution in sight for the war, which has caused massive destruction and forced nearly half the Syrian population to flee their homes.
‘Fierce economic war’
Syrian warplanes on Sunday launched fresh strikes on rebel strongholds on the edge of Damascus, some of which used highly destructive barrel bomb attacks, a monitoring group said.
"Warplanes carried out two air strikes against areas of Douma," northeast of Damascus, the Syrian Observatory for Human Rights said adding that 13 people, including three children and three women, were killed in that particular raid.
The raids came as fighting raged on the edges of Daraya between rebels and the army, which for more than a year has battled to secure the capital.
On the economic front, Prime Minister Wael al-Halqi said on Sunday a "fierce economic war" was behind the sharp fall in the value of the Syrian pound against the US dollar.
"A fierce economic war ... is being waged against the national economy aimed at destabilising the Syrian pound," he said, quoted by state news agency Sana.
The pound was trading on Sunday at 176 against the dollar, compared to 156 last week, in a trend which has seen it lose more than three-quarters of its value against the US currency since March 2011.
Central bank governor Adib Mayaleh said his institution would sell around $20m on 21 April in an effort to support the Syrian pound.
Syria 'targeted for its influence'
Since the start of a revolt against Assad in 2011, Damascus has blamed all violence in the country on a foreign-backed "terrorist" plot, denying the existence of any grassroots movement for political change.
Like its allies Iran and Lebanese Shi’ite movement Hezbollah, the government has said the violence in Syria is rooted in a bid to break the anti-Israel "resistance axis".
Assad said the country "is not only being targeted because of its geo-political significance... but because of its historic role in the region and its big influence on the Arab street".
Syria, he said, "is subject to a bid to take control of its independent decision-making, and an attempt to change its policy from one that suits the Syrian people's interests, rather than the interests of the United States and the West's interests in the region."
On Sunday, Assad reiterated his belief that Israel "has played a key role in supporting the terrorist groups".
Lebanon's Hezbollah, a strategic ally of Assad's government which has sent thousands of fighters into Syria, has played a key role in helping turn the tide in Assad's favour.
A series of truces have also been agreed, mainly in southern Damascus and the outskirts of the capital.
The ceasefires came after months of suffocating army sieges that had led to the deaths of scores of people, as a result of medical and food shortages.
The agreements stipulate rebels should hand over their heavy weapons in exchange for aid deliveries, but opposition activists in some areas where truces have been reached have accused the government of violating the deals.
Syria's conflict broke out after the government unleashed a brutal crackdown against an Arab Spring-inspired peaceful protest movement.