Since the July 24 announcement, Turkey has launched several waves of airstrikes against elements of a Kurdish separatist group known as the P.K.K., which is widely listed as a terrorist group. But that group and its allies in Syria, who have been closely working with American forces, are pushing Islamic State militants out of areas they once controlled.So while the United States had long sought Turkey’s help in fighting ISIS, the events since the agreement reveal the tangle of diverging interests in the region.

Kurds ↔ U.S.

Coordinating Against ISIS

Kurdish fighters have been coordinating with the American military since last October. From cloaked rooms in northern Syria, members of the militia known as the Y.P.G. have relayed intelligence and coordinates for potential airstrike targets to an American operations center hundreds of miles away.The resulting strikes have in turn helped the Kurds seize a broad stretch of territory along the Turkish border from the Islamic State. “The role of the coalition jets has been essential to these victories,” said Idris Nassan, a senior Kurdish official from Kobani.

Y.P.G. control, May 28, 2015

Y.P.G. gains since May

ISIS control

TURKEY

Adana

Incirlik

air base

Gaziantep

Qamishli

Kobani

Jarablus

Kilis

Government

controlled

Tal Abyad

Ras al-Ain

Manbij

Al Bab

Aleppo

IRAQ

Hasaka

Ain Issa

SYRIA

Area

of detail

Raqqa

SYRIA

25 MI

TURKEY

Adana

Incirlik

air base

Gaziantep

Qamishli

Kobani

Jarablus

Kilis

Government

controlled

Tal Abyad

Ras al-Ain

Manbij

Al Bab

Hasaka

IRAQ

Ain Issa

Aleppo

SYRIA

Area

of detail

Raqqa

SYRIA

25 MI

Area

of detail

SYRIA

TURKEY

Adana

Incirlik

air base

Qamishli

Kobani

Jarablus

Tal Abyad

Ain Issa

Hasaka

Aleppo

Raqqa

IRAQ

SYRIA

50 MI

Area

of detail

TURKEY

Incirlik

air base

SYRIA

Kobani

IRAQ

SYRIA

50 MI

The New York Times|Sources: Institute for the Study of War; Kurdish officials

The Y.P.G. is perhaps America’s most effective ally in Syria against the Islamic State. But American officials, though they will broadly acknowledge that they are working with the Y.P.G., take pains not to detail just how closely the forces are working together, given the group’s ties to the outlawed P.K.K.

Kurdish Y.P.G. fighters check maps as they coordinate an airstrike on an Islamic State position in Hasaka. Mauricio Lima for The New York Times
Turkey ↔ U.S.

Allies, but With Conditions

The United States has sought Turkey’s help in the fight against ISIS since last year. Turkey, which has been a NATO member since 1952 and is considered by American officials to be critical to weakening the Islamic State in Syria, was reluctant to participate. Turkey finally agreed to assist, but with some conditions, including the creation of an ISIS- and Kurdish-free zone in Syria on the Turkish border.In return, the United States will be allowed to launch military operations against the Islamic State from Incirlik Air Base and other bases in Turkey “within a certain framework,” according to President Recep Tayyip Erdogan. American officials have been careful not to offend Turkey and have publicly supported its campaign against the P.K.K..In a statement on Twitter, Brett H. McGurk, President Obama’s envoy to the coalition fighting the Islamic State, said, “We fully respect our ally Turkey’s right to self-defense.”

Y.P.G. control

ISIS control

TURKEY

Adana

Incirlik

air base

Gaziantep

Qamishli

Kobani

Jarablus

Kilis

Government

controlled

Tal Abyad

Ras al-Ain

Manbij

Al Bab

Aleppo

Hasaka

Ain Issa

IRAQ

SYRIA

Approximate zone where U.S. and Turkish forces seek to clear ISIS militants.

Area

of detail

Raqqa

SYRIA

25 MI

TURKEY

Adana

Incirlik

air base

Gaziantep

Qamishli

Kobani

Jarablus

Kilis

Government

controlled

Tal Abyad

Ras al-Ain

Manbij

Al Bab

Hasaka

IRAQ

Ain Issa

Aleppo

SYRIA

Area

of detail

Approximate zone where U.S. and Turkish forces seek to clear ISIS militants.

Raqqa

SYRIA

25 MI

Area

of detail

SYRIA

TURKEY

Adana

Incirlik

air base

Qamishli

Kobani

Jarablus

Tal Abyad

Ain Issa

Hasaka

Aleppo

Approximate zone where U.S. and Turkish forces seek to clear ISIS militants.

Raqqa

IRAQ

SYRIA

25 MI

Area

of detail

TURKEY

Incirlik

air base

SYRIA

Kobani

SYRIA

IRAQ

Approximate zone where U.S. and Turkish forces seek to clear ISIS militants.

50 MI

The New York Times|Sources: Institute for the Study of War; Kurdish officials
Kurds ↔ Turkey

Suspicion and Violence

Analysts say that Turkey’s decision to join the fight against the Islamic State was driven in part by the threat posed by the Y.P.G.’s rapid territorial gains within Syria. Kurds across the region have historically sought an independent state, which the Turkish government strongly opposes. Mr. Erdogan has said that Turkey “will never allow the establishment of a new state on our southern frontier in the north of Syria.”

Some areas of violence between Turkey and the P.K.K. since March 2013

Areas of Turkish airstrikes on P.K.K. positions, July 24 to August 3

Kurdish-inhabited areas

Area of

detail

Armenia

Kayseri

Bingol

Turkey

Mus

Diyarbakir

Siirt

Iran

Orumiyeh

Adana

Gaziantep

Kobani

Iraqi

Kurdistan

Iraq

Hasaka

Aleppo

Syria

Mosul

50 MILES

Raqqa

Area of

detail

Armenia

Turkey

Iran

Diyarbakir

Orumiyeh

Adana

Kobani

Iraqi

Kurdistan

Mosul

Syria

Aleppo

Iraq

50 MILES

100 MI

Turkey

Area of

detail

Syria

Iraq

Area of

detail

Turkey

Kayseri

Adana

Gaziantep

Mosul

Iraqi

Kurdistan

Syria

Iraq

100 MI

The New York Times|Sources: International Crisis Group (airstrikes and areas of violence); Michael Izady, Columbia University’s Gulf 2000 project (Kurdish areas)

For now, Turkey is more actively targeting Kurdish insurgents with the P.K.K. than it is fighters with the Islamic State. In Turkey’s recent roundup of 1,300 people it identified as terrorism suspects, 137 of those arrested were linked to the Islamic State and 847 were linked to the P.K.K. At the same time, Turkey bombed P.K.K. positions in southeastern Turkey and northern Iraq, claiming that the militants could attack Turkish areas from across the border.The Turkish airstrikes effectively ended a two-year cease-fire with the P.K.K. and has set off rounds of protests and clashes between Turkish security forces and Kurdish militants throughout Turkey. In the meantime, Turkish operations against the Islamic State have been slow to develop.Mr. Erdogan’s strategy, according to analysts, is also politically motivated. In June, his party lost its parliamentary majority partly because of the electoral success of a pro-Kurdish party. By bombing the P.K.K., Mr. Erdogan stands to win back votes of nationalists who oppose Kurdish autonomy.

Turkish airstrikes hitting P.K.K. targets in northern Iraq in late July. Reuters
Correction: Aug. 14, 2015

An earlier version of this article misstated the day that Turkey announced that it would help fight the Islamic State. It was July 24, not June 24.