WASHINGTON — The Obama administration is weighing a military plan to directly arm Syrian Kurdish fighters combating the Islamic State, a major policy shift that could speed up the offensive against the terrorist group but also sharply escalate tensions between Turkey and the United States.

The plan has been under discussion by the National Security Council staff at a moment when President Obama has directed aides to examine all proposals that could accelerate the fight against the Islamic State, also known as ISIS or ISIL. Mr. Obama has told aides that he wants an offensive well underway before he leaves office that is aimed at routing the Islamic State from Raqqa, the group’s de facto capital in northern Syria.

Deciding whether to arm the Syrian Kurds is a difficult decision for Mr. Obama, who is caught in the middle trying to balance the territorial and political ambitions of Turkey and the Syrian Kurds, two warring American allies that Washington needs to combat the Islamic insurgency.

Directly providing weapons for the first time to the Syrian Kurds, whom American commanders view as their most effective ground partner against the Islamic State, would help build momentum for the assault on Raqqa. But arming them would also aggravate Mr. Obama’s already tense relations with Turkey’s president, Recep Tayyip Erdogan. The United States and Turkey sharply disagree over Syria’s Kurdish militias, which Turkey sees as its main enemy in Syria.