(CNN) Millions of refugees from Syria have flooded into Turkey, straining its economy and draining resources. Turkey has been drawn into its neighbor's 5-year-long war , spawning discord with Russia. Its leaders have pushed to join the European Union while fending off criticism of cracking down on opponents and journalists.

On top of all this, Turkey is battling a terrorist insurgency.

In the latest violence, a Kurdish rebel group on Thursday claimed responsibility for a car bomb attack that killed at least 37 people earlier this week in the capital.

The Kurdistan Freedom Falcons, or TAK -- an offshoot of the Kurdish separatist group PKK -- said on its website that militants struck Sunday "in the heart of (the) fascist Turkish republic."

What are the Kurdish factions in Turkey and Syria?

What are the Kurdish factions in Turkey and Syria? 01:29

What are the Kurdish factions in Turkey and Syria?

The TAK said "our comrade" Seher Cagla Demir was the female suicide bomber behind the Ankara attack. Turkey's Interior Ministry also identified Demir as the bomber, saying she's believed to have trained with Syria-based Kurdish rebels known as the YPG.

Turkey's NATO allies haven't labeled the YPG as a terrorist group. The U.S.-led coalition supports this Kurdish group and considers it a reliable and effective ally in the fight against ISIS in Syria, much to the chagrin of Turkish President Recep Tayyip Erdogan.

Erdogan: Attacks 'boost' Turkey's resolve

The PKK, or Kurdistan Worker's Party, which seeks an independent state in Turkey, has been in an armed struggle with Turkey for decades and has been designated a terrorist organization by Turkey, the United States and EU.

There have also been crackdowns in restive Kurdish areas in southeastern Turkey, with some towns put under curfew. Some accuse the Turkish government of unfair collective punishment for the crimes of a few, saying security forces have acted with impunity and killed civilians.

The carnage has spread to Turkey's most populated cities.

In January, 10 German tourists died in a suicide bombing in Istanbul's Sultanahmet Square. Authorities connected this attack to ISIS, the terror group that has taken over swaths of Syria and Iraq.

Then came a February bombing targeting military vehicles in central Ankara , killing 28 people and wounding 61 others.

Top PKK leader Cemil Bayik said his group didn't know who was responsible. But the Kurdish Freedom Falcons later claimed it carried out the attack as "revenge" for Turkish military actions and warned that tourists could be next.

Over the weekend, a blast ripped through a major transit hub in Ankara. Citing a security source, Turkey's semiofficial Anadolu news agency reported Thursday that the 660-pound (300-kilogram) bomb of RDX, TNT and ammonium nitrate used in the attack was similar in makeup and scale to one used a month earlier, a few hundred meters away.

"Terror organizations and their pawns are targeting our innocent citizens in the most immoral and heartless way as they lose the fight against our security forces," Erdogan said in a statement this week.

"Terror attacks -- which intend to target the integrity of Turkey, unity and solidarity of our people -- do not diminish our will to fight against terror, but further boost it."

What is the TAK?

The TAK is not technically a part of Turkey's main bete noir of Kurdish terrorism, the PKK, but some analysts say that's partly a matter of plausible deniability.

They say the TAK follows the broad direction of the PKK, adhering to its ceasefires and mimicking its targeting, but does not seek approval from the PKK's hierarchy for each attack.

The PKK's critics say that this loose structure allows the main Kurdish group to keep acts of carnage perpetrated against victims -- like the Ankara attack, which killed almost exclusively innocent civilians -- at an acceptable distance from the larger militant group.

The fact that a faction linked, however loosely, to the PKK has claimed this savage attack will still massively complicate the U.S. ties with Turkey.

The United States arms and assists Kurds fighting in northern Syria against ISIS.

But Turkey insists these militants in northern Syria, the YPG, are essentially the PKK in different uniforms.

The U.S. disputes that and lists the PKK as a terror group. But this gray area has damaged relations between Ankara and Washington, and the civilian massacre in Ankara will further complicate that vital relationship in the war against ISIS.

Turkey may get even more refugees

Other governments have taken precautions as Turkey faces the threat of more terror attacks that could drive tourists away and hurt its economy.

In December, the U.S. diplomatic mission in Turkey cautioned Americans to avoid its consulate in Istanbul because of a security threat. And last week, the American Embassy in Ankara warned of a possible terrorist plot to strike government buildings in the capital's Bahcelievler neighborhood, a few minutes' drive from the site of Sunday's explosion.

Germany's Foreign Ministry said Thursday that the German Embassy in Ankara, a German school in the city and the German Consulate in Istanbul remained closed "based on a possible threat that we are still investigating."

This warning comes as German Chancellor Angela Merkel has taken a leadership role in working with Turkey on how to deal with 4.8 million refugees, as reported by the United Nations , who have fled violence and persecution in Syria.

The majority of those, more than 2.7 million refugees , have ended up in Turkey. Others have tried to escape deeper into Europe, sometimes putting their lives in the hands of human smugglers.

Turkey and the EU have been discussing a proposal to expedite Turkey's entry into the union, to send refugees who left Turkey for Greece back to Turkey and to provide Ankara with financial aid to deal with this influx.

Donald Tusk, the European Council president, spoke Wednesday of working toward "an agreement to further strengthen our cooperation with Turkey in order to stem the flow of migrants from Turkey to Europe."

Merkel, addressing her nation's legislature, also talked about "deepened cooperation" with Turkey and called Ankara's "demand for more financial help completely understandable."

At the same time, she said any discussions about migrants shouldn't take place in a vacuum. The other things happening in Turkey -- including criticisms of rights violations and its crackdown on Kurds -- matter, too.

"It ... goes without saying that we stress to Turkey, for example, the importance of freedom of the press (and) the freedom of the Kurds," Merkel said Wednesday. "As important as the necessary fight against the PKK's terror is, (Turkey must take a measured) approach ... for all Kurds."