Turkey on January 20 launched the "Olive Branch" operation against Syrian Kurdish People's Protection Units (YPG) militia which Ankara sees as a terror group and a threat to Turkish territory.
The Turkish army and allied Ankara-backed Syrian rebel forces are seeking to oust the YPG from its western border stronghold of Afrin but the operation so far has been marked by fierce clashes.
The army said that one of the soldiers was killed in a clash and another on the border area, without giving further details.
President Recep Tayyip Erdogan said on Thursday the Turkish army and Ankara-backed rebels had suffered 25 fatalities between them in the operation so far.
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Meanwhile, seven civilians have been killed in mortar fire on the Turkish side of the border that Ankara blames on the YPG.
Ankara says that hundreds of YPG fighters have been killed in the operation so far but it is not possible to verify this.
Turkey says the YPG is an offshoot of the outlawed Kurdistan Workers' Party (PKK) which has waged a three-decade insurgency against the Turkish state.
The offensive by Washington's fellow NATO member Ankara on a US-allied force has even raised fears of a military confrontation between two alliance powers.