"I do know that yesterday the President authorized the Department of Defense to equip Kurdish elements of the Syrian Democratic Forces as necessary to ensure a clear victory over ISIS in Raqqa, Syria", he said.
On April 27, Turkish warplanes struck YPG forces in Syria and also hit Kurdish forces in neighboring Iraq in what Ankara described as "terrorist havens".
Tabqa sits on the Euphrates as well as a strategic supply route about 55 km (35 miles) west of Raqqa.
SDF spokesman Talal Silo said they were able to capture Tabqa "thanks to the sacrifices of the SDF's heroes and with the full, unlimited support of the USA -led global coalition", Reuters reported.
The dispute could ignite more fighting between the two key American allies in the battle against the extremist group as Syrian Kurdish forces gear up for a major operation to drive the militants from their de facto capital, Raqqa.
Mattis met in London with Turkish Prime Minister Binali Yildirim on the sidelines of a security conference on Somalia a day after Turkish President Recep Tayyip Erdogan accused the us of siding with terrorists by giving small arms, ammunition, mortars and shoulder-fired weapons to the Syrian-Kurdish YPG, or People's Protection Units.
USA officials have also tried to assure Turkey that the Kurdish fighters will not play a role in stabilizing the city after the offensive, instead leaving that task to local Arabs.
Although U.S. officials have said repeatedly since then that the war against the Islamic State group in Syria remains the priority, that strike - coupled with the buildup of forces in the north - has raised speculation of longer term U.S. ambitions in Syria and concerns about a more permanent project.
Turkish President Recep Tayyip Erdogan called on the U.S.to reverse its decision, saying weapons in the hands of the Kurdish-led forces are a "threat" to his country. It was the first time the US has attacked Syrian forces in the six-year civil war.
Ilham Ahmed, a top official in the Syrian Democratic Forces' political office, said the decision to provide heavier arms carries "political meaning" and "legitimises the YPG and the Syrian Democratic Forces".
Ankara strongly opposes US support of the YPG, viewing it as the Syrian extension of the outlawed Kurdistan Workers Party (PKK), which has waged a three-decade insurgency inside Turkey. The U.S. and other Western nations also view the PKK as a terrorist group.
Turkey's top diplomat has criticized a US decision to provide arms to Syrian Kurdish fighters, saying every weapon given to them poses a threat to Turkey.
The statement said that in the final days of the battle, around 70 IS fighters withdrew from the town, leaving heavy weapons behind them. The move allowed for the dismantling of land mines around the dam.
About 30,000 Tabqa residents have been displaced since fighting began in late March.
On Wednesday, the Democratic Forces said fighters captured the country's largest dam from the Islamic State militants.
The Kurdish YPG militia meanwhile welcomed the us decision to arm its forces in the battle against Islamic State in Syria, saying this would be a significant boost in the war against terrorism.