Yilmaz, cited by the Anadolu news agency, referred to the program, which is expected to take place in Turkey, Jordan, Qatar and Saudi Arabia.
The program that plans to train about 5,000 Syrian fighters annually was supposed to start in March, weeks after Washington had signed a deal with Ankara. However, on Friday, Turkish Foreign Minister Mevlut Cavusoglu said that the program was delayed by Washington.
On Thursday, the United Kingdom announced its plans to join US-led efforts to fight ISIL by sending to Turkey about 75 military trainers and staff to teach the use of small arms, infantry tactics and medical skills to Syrian opposition forces.
UK Defense Secretary Michael Fallon said that although the responsibility for fighting the Islamic State lies with the Syrian forces, the UK will teach them military techniques.
An international coalition, comprising more than 60 countries, is conducting airstrikes on ISIL positions in both Syria and Iraq.
In January, US State Department spokeswoman Jen Psaki said that Washington expected the coalition-trained moderate opposition in Syria to fight against both the country's president Bashar Assad and the Islamic State militants.