Mattis, in acknowledging the YPG to be essential to the US-led coalition's victory over Daesh in the face of Ankara's demands, will meet with Fikri Isik, the Turkish Minister of Defense, in Brussels on Thursday.
Turkish officials late last week said Mattis had reassured them by letter that arms given to the Syrian Kurds would be taken back and that the US would provide Turkey with a regular list of arms give to the fighters. "The closer we get, the more complex it gets".
Washington launched a retaliatory cruise missile strike days later against Syria's Shayrat airbase from where it said the chemical attack was launched, the first direct U.S. action against the regime.
Earlier this month, the Syrian Observatory for Human Rights said US-led coalition airstrikes on two Syrian provinces targeting extremists have killed 472 civilians over the past month, more than double a previous 30-day toll.
"As long as it's worked out by the commanders and enough people know about it in sufficient time there are ways that have proven that we can do this", Mattis said.
It depends, he said, on the battle and what weapons the Kurdish fighters need. "We try to end that through diplomatic means".
In April, President Trump ordered a cruise missile strike in response to what Washington claimed was a gas attack carried out by Assad's forces that killed almost 90 people.
"If. Mr Assad conducts another mass murder attack using chemical weapons, he and his military will pay a heavy price", White House spokesman Sean Spicer said in a statement. Assad's government and his allies deny the allegation.
The U.S. accused Syrian forces of launching a chemical attack from the base in April that killed dozens of civilians.
USA forces would not fire on targets "unless they are the enemy, unless they are ISIS", he said late on Monday.
Mattis did not address the nature of the intelligence or White House warning as he flew to Europe for a North Atlantic Treaty Organisation meeting, but said the USA was not going to get pulled into the conflict between the regime and the armed opposition.
Turkey sees the YPG as an extension of the outlawed Kurdish PKK, which has been waging an insurgency in the country's southeast since the mid-1980s. The Turkish government is concerned that the US arms and equipment given to the YPG will end up in the hands of the PKK.
Kurdish People's Protection Units (YPG) fighters walk with their weapons at the eastern entrances to the town of Tal Abyad in the northern Raqqa countryside, Syria, June 14, 2015, after taking control of nearby Suluk town from ISIS fighters.