Mattis, the USA defense secretary, said on May 10 that the United States had had very open discussions with Turkey.
US special operations forces are embedded with the Kurdish-led fighters known as the Syrian Democratic Forces as they prepare for battle around Raqqa.
Turkey, the US and other Western allies view the PKK as a terrorist group.
Washington is trying to provide Turkey assurances.
The news about the USA plan to arm Syrian Kurds comes, as the Trump administration mulls sending as many as 5,000 more troops to Afghanistan, a military official told NBC News, and as the White House makes moves it believe will help American forces "start winning" again in the region. "Our wish is that the US stops this wrong and does what is mandated by our friendship".
It has also voiced concern that weapons given to the YPG would end up in the hands of the PKK.
Turkish officials are asking the USA to reconsider its decision to arm a Kurdish militia group in Syria, which they claim is a terrorist organization.
Turkey's prime minister Wednesday criticized Washington's decision to arm a Syrian offshoot of the terrorist PKK to fight Daesh in Syria. "We do not ever give weapons to the PKK".
"We are carrying out, and will carry out, all necessary diplomatic communications", Canikli said.
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The decision comes despite sharp objections from Turkey. "Otherwise, the outcome won't only affect Turkey, a negative outcome will also emerge for the United States".
Hurriyet newspaper quoted Canikli as saying Wednesday: "The United States is providing every kind of aid to the PKK through (Syrian Kurdish forces)".
Mattis has played down the friction between the allies, saying that while "it's not always tidy", they will resolve any differences.
The decision came ahead of Erdogan's planned trip to the White House coming week, during which, Erdogan said, he would personally address Turkey's concerns.
But their meeting was impossible to separate from the Trump administration's unfolding political drama in Washington, where FBI and congressional investigations are looking into possible collusion between Trump campaign associates and the Kremlin related to the 2016 election.
One U.S. official, speaking on condition of anonymity, said the equipment for the Kurdish fighters could include small arms, ammunition, machine guns, armored vehicles and engineering equipment.
The U.N. has warned damage to the Tabqa dam - Syria's largest - could lead to massive flooding, and a source who works with the dam's technicians said they had fled the structure as fighting drew near in recent days. The would-be safe zones would not cover areas where the US -led coalition is fighting IS.