The plane went down in the Mediterranean last month and the two pilots have not been found.
The incident has heightened tensions between the two countries.
Last week, Turkish PM Recep Tayyip Erdogan condemned Syria's action and described the neighbouring country as a "clear and present threat".
Turkey's border areas were reinforced with rocket-launchers and anti-aircraft guns on Friday.
It has also emerged that the Turkish air force scrambled fighter jets on Monday for the third day in a row after Syrian helicopters were said to have approached the border.
AnalysisIn saying that he "regrets the incident 100%", Syrian President Bashar al-Assad is seeking to reduce tensions with Turkey and turn the page on an episode that risked bringing the two countries to the brink of war.
However, this falls well short of an apology. President Assad is still sticking to Syria's story that the plane was engaged in Syrian airspace, something the Turks dispute.
Mr Assad sought to deflect criticism by saying that the plane was flying at low level "in an air corridor used three times in the past by the Israeli air force". The soldier who shot it down, he said, had no radar and could not know to which country the plane belonged.
But did this really look like an Israeli attack? And surely somebody in Syria's comprehensive air defence network was monitoring the plane on radar.
In other developments:
- Turkish media reported late on Monday that another 85 Syrian soldiers, including 14 senior officers, had defected across the Turkish border. It is one of the biggest groups of army defections since the March 2011 uprising in Syria began
- Syria is practising a widespread policy of state-sanctioned torture with an "archipelago of torture centres", a Human Rights Watch report says
- UN human rights chief Navi Pillay has said that both Syrian government forces and the opposition have been involved in operations that harmed civilians
- At least 78 people were killed in violence throughout Syria on Monday, opposition activists reported
- Clashes were reported on Tuesday in suburbs of Damascus and government forces were operating in the cities of Deraa and Deir al-Zour, the Local Co-ordination Committees (LCC) activist group said
- UN observers visited the Damascus suburb of Douma on Tuesday, which was recaptured days earlier by government forces. They turned back for security reasons. Although their mission in Syria is officially suspended, they carry out humanitarian visits to assess the effect of the crisis on civilians
- A picture released by activists purportedly showed the burial of more than a dozen people killed by Syrian forces in Douma
End Quote Bashar al-Assad Syrian presidentI would never wish this on any plane but an enemy one. And in the case of a Turkish plane I am saying 100%, 'If only this had not happened' ”
The soldier who opened fire on the F-4 Phantom had no access to radar, he says, pointing out that the same route was used in the 2007 Israeli bombing of a site in north-eastern Syria.
The UN's nuclear agency later said the site was very likely a nuclear reactor under construction.
Downed Turkish jet: the two accounts
|Syrian version||Turkish version|