A US official, speaking on condition of anonymity, clarified that Mattis was not signaling a new agreement on a Turkish role in the offensive or any decision on whether to arm the Kurdish fighters.
But the USA sees the Kurdish group as its most reliable partner in the fight against ISIS in Syria.
There has been wide support from senior USA military officials to provide direct arms to Syrian Kurdish forces, but sensitivities about Turkish opposition has delayed such a decision.
"We are keenly aware of the security concerns of our coalition partner Turkey", said White in the statement.
Pressed about the matter, Mattis said he did not want to disclose USA battlefield plans but suggested confidence that Washington and Ankara would get past the impasse.
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The U.S., however, views the Kurdish forces in Syria as some of the country's best fighters, and necessary to the upcoming offensive to retake Raqqa, the northeast Syrian city which ISIS considers its capital.
After months of brutal, street-by-street combat, IS has now lost control of most of its stronghold of Mosul in Iraq, while the jihadists have become largely isolated in Raqa.
White acknowledged Turkey's concerns, but said "the U.S.is committed to preventing additional security risks and protecting our North Atlantic Treaty Organisation ally".
Other officials said Trump's authorisation includes safeguards meant to reassure Ankara that the additional U.S. weaponry and equipment will not be used by the Kurds in Turkey.
The Pentagon chief said he had useful discussions with Turkey and described the two countries as working out differences over the US' alliance with Syrian Kurds. The Turks have insisted that the Syrian Kurds be excluded from that operation, but US officials insisted there was no real alternative.
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Under Secretary of State Tom Shannon also had a closed meeting with Turkish presidential adviser Ibrahim Kalin Tuesday at the State Department.
"The United States condemns the Assad regimes use of brutal violence and human rights abuses and calls on the Assad regime to stop its violence against the Syrian people, uphold the Cessation of Hostilities, enable the delivery of humanitarian assistance, and allow a political transition in Syria that will forge a credible path to a future of greater freedom, democracy, opportunity, and justice", said the US President.
Turkey carried out a series of airstrikes against the YPG last month, a move that drew immediate complaints from United States officials. The Kurdish group in Syria said 20 of its fighters and media activists were killed in the strike, which was followed by cross-border clashes.
"We've been conducting military and diplomatic dialogues with the Turks and it was a very, very useful discussion today", Mattis told reporters Tuesday following the meeting, while not addressing the issue of arming the Kurds directly.
Baldor reported from Copenhagen and from Vilnius, Lithuania.
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