Assad expressed the hope that tensions would not escalate further.
The Syrian president's comments, which fell short of an apology, came as officials in Ankara revealed that Turkey had again scrambled F16 fighters on Tuesday – for the third time in as many days – after Syrian transport helicopters flew near its border. Turkey has also deployed anti-aircraft missiles.
On a day that brought more violence on the ground across Syria and continuing diplomatic pressure on Damascus, Assad made clear he was feeling the heat from the deterioration in relations with Turkey.
But the president said the Turkish Phantom jet had used the same route as Israeli planes in the past.
"We learned it belonged to Turkey after shooting it down. I say 100% 'if only we had not shot it down'," Cumhuriyet newspaper quoted him as saying. "We are in a state of war, so every unidentified plane is an enemy plane."
Reports from Syria described shelling in Douma, Talbiseh and Rastan, near Damascus, and in Homs, in the centre of the country.
Activists reported at least 25 civilians killed, at least nine of them in Homs. A convoy carrying UN observers in Syria headed towards Douma to visit hospitals but turned back for security reasons.
'Long, bumpy road'
Opposition sources reported that 114 people had been killed on Monday.
In Geneva, a spokesperson for Kofi Annan, the UN-Arab League envoy to Syria, said that the outcome of last weekend's international conference on Syria was a shift in the positions of Russia and China – even though the final communiqué avoided the crucial issue of whether Assad would have to step down to allow the creation of a "transitional unity government … on the basis of mutual consent".
Diplomats said that an earlier draft text was watered down at Russia's insistence.
"It's going to be a long, bumpy, road," said Ahmad Fawzi. "But we believe that commitments made in Geneva were genuine and if applied as promised will have an effect. Let's wait until the dust settles on this agreement and … everyone will see that it was quite an accomplishment."
But France's foreign minister, Laurent Fabius, revealed that Russia would not be attending a meeting of the western-Arab Friends of Syria grouping in Paris on Friday, even though there was an invitation.
Moscow and Beijing accuse the US and its allies of pursuing "regime change" in Syria and insist that only Syrians can decide on the country's political future.
Fabius said: "Bashar Assad is a slaughterer and the sooner he leaves the better."
The German foreign minister, Guido Westerwelle, said, after talks with Fabius, that Assad's acts had been "unpardonable" and that his reign "must end".
Westerwelle goes to Moscow on Thursday to persuade Russia to take a firmer stand against Assad.
Britain's foreign secretary, William Hague, said in a statement that the new Human Rights Watch report on torture in Syria highlighted the horror of the situation.
"The scale of the barbaric acts that are being carried out by the regime against the population is appalling," Hague said.
Asked by Cumhuriyet under what terms he might agree to 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."
Syrian opposition groups, meeting in Cairo under the auspices of the Arab League, have faced divisions over the way ahead.
But the head of the largest group, the Syrian National Council, Abdul Basset Sieda, has said he is preparing a "road map" to lay down the rules for a post-Assad transition. – © Guardian News and Media 2012