Turkey launched the military operation on the Kurdish-held enclave of Afrin in northern Syria on January 20, citing national security.
Speaking at a meeting of the ruling Justice and Development Party (AKP) in Istanbul, Erdogan said "we might lose one helicopter, but they will pay a heavier price".
Turkish Prime Minister Binali Yildirim announced the deaths in a televised address on Saturday.
However, in a posting on Twitter, Mustefa Bali, spokesman for the US-backed Syrian Democratic Forces dominated by the YPG, said a helicopter had been hit in the Rajo area of northwest Afrin, near the Turkish border.
The YPG claimed they brought down the helicopter, but Turkish officials did not confirm that account.
In a statement, the military said the Turkish Armed Forces had destroyed 19 YPG targets and "neutralized" 86 more militants during operations since February 10. Calling for "urgent worldwide action" to protect civilians, Zeid also slammed what he called an "epic failure of global diplomacy" to end the seven-year-old war. It's determined to prevent the establishment of a Kurdish state across the border in Syria and has used military force in the past against Kurds and ISIS in the northern part of the neighboring country.
The U.S.'s Syria policy, especially its military support for the Syrian Democratic Forces (SDF), which is dominated by YPG terrorists, has been a cause of tension between the two North Atlantic Treaty Organisation allies.
Murat Karayilan, a member of the PKK's Executive Council, told the pro-Kurdish Firat News Agency that Turkey was telling "lies" about the extent of the casualties it had suffered and number of YPG fighters killed.