Another 13 were injured in the clashes on Thursday, with several said to be in a critical condition.
It is one of the bloodiest days for Turkish troops since they began a major offensive against Kurdish fighters in Afrin in January.
More than 580 people have reportedly been killed in the rebel-held enclave near Damascus since the Government and its allies intensified a bombardment on 18 February.
About 393,000 civilians trapped there also face severe shortages of food and medical supplies.
The debate in Geneva, expected later on Friday, was requested by the UK. A draft resolution, seen by Reuters news agency, strongly condemns the “denial of humanitarian access” and “repeated attacks against medical facilities”.
Five “heroic comrades fell as martyrs and seven were wounded”, the first statement said. A second statement announced three more soldiers had been killed and six more wounded.
No official details of the clashes were given but the private Dogan news agency says Kurdish fighters used tunnels to ambush Turkish special forces in the Keltepe district.
A Turkish helicopter sent in to rescue the wounded was hit and had to turn back, the report adds.
The Turkish Government says the People’s Protection Units (YPG) militia is an extension of the banned Kurdistan Workers’ Party (PKK), which has fought for Kurdish autonomy in south-eastern Turkey for three decades.
The YPG denies any direct organisational links to the PKK.
Neither side has released much information about fatalities, making the death toll in Afrin difficult to gauge.