The statement said that since the beginning of the operation 13 Turkish soldiers had been martyred and 57 wounded.
In a later statement, it added a Turkish army tank had been hit in another attack, killing all five servicemen inside.
Turkish forces immediately responded to attacks with Fırtına howitzers.
Since the start of the operation, the PYD/PKK has carried out cross-border attacks on Turkey by firing rockets on civilian neighborhoods.
Turkish authorities said on Friday they had detained eight people in connection with a bomb that rocked the capital Ankara on Thursday, injuring three people.
"The Turkish government should issue standard instructions to the border guards at all crossing points that lethal force must not be used against asylum seekers and no asylum seeker is to be mistreated, but should be given access to medical aid when required", HRW said.
During the conversation, Erdogan said Turkey does not have any design on any country's territory and added the operation was aimed at clearing PYD/PKK, YPG and Daesh terrorists from Afrin.
Erdogan's spokesman Ibrahim Kalin meanwhile told journalists in Istanbul that the operation was going as planned but there was no timetable for its duration and it would "continue until we clear all those areas". Turkey considers the YPG a "terrorist" group.
But the YPG has been working closely with the United States to fight the Islamic State extremist group in Syria.
The Turkish army on Saturday announced the killing of seven of its soldiers taking part in Ankara's "Operation Olive Branch" offensive to dislodge US-backed Kurdish forces from the Afrin enclave in northwestern Syria.