Syrian President Bashar al-Assad regrets that Syrian forces shot down a Turkish jet last month and said he would not allow the tensions between the two countries to turn into open combat, according to an interview with a Turkish newspaper.

"We learned that it belonged to Turkey after shooting it down. I say 100 per cent: 'If only we had not shot it down'," Assad told Cumhuriyet, a daily newspaper, in an interview published on Tuesday.

His comments emerged as fighting raged throughout the country. On Monday, Syrian helicopters bombarded a Damascus suburb, and Turkey again scrambled warplanes near the border in the north.

Asked whether the tensions between Syria and Turkey could lead to war, Assad said: "We will not allow (the tensions) to turn into open combat between the two countries, which would harm them both."

He also said Syria had not amassed and would not amass military forces along the Turkish border, whatever action Turkish Prime Minister Tayyip Erdogan's government takes.

The paper did not specify when the interview was held, but in it Assad refers to an international meeting held in Geneva on Saturday under the auspices of peace envoy Kofi Annan.

Turkey has heightened military activity along the border since Syria shot down the Turkish jet over the Mediterranean on June 22, prompting a sharp rebuke from Ankara, which said it would respond "decisively".

Syria says it shot down the Turkish jet in self-defence and that it was downed by an anti-aircraft gun with limited range in Syrian air space. Turkey says the jet accidentally violated Syrian air space for a few minutes but was brought down by a surface-to-air missile in international air space.

Assad said Syria would not shy away from apologising if it emerged that the plane was shot down in international airspace.

"The plane was using a corridor which Israeli planes have used three times in the past. [Syrian] soldiers shot it down because we did not see it on our radar and because information was not given," he said. "Of course I might have been happy if this had been an Israeli plane."

“If the Turkish government had not cut military relations [with Syria] we would have discussed this matter between military authorities,” Assad said in the interview.

“We would have solved it before it got this big. But in recent months, we do not have a number of a Turkish commander to call in case of emergencies.”

When asked under what terms he might leave office, Assad replied, "Why would I hold on to power if saving my people and my country was a question of me staying or leaving? I would not stay even for one day."

Assad added that if "my people don't want me, then there are elections. If people want they can make me leave."