Simple answer, yes, deaths happened in both directions, but the only genocide occurring was of the Armenians, not of Turkish people. Portrayal of the contrary should be disregarded as apologism. For more, check out the FAQ section we have on this.

First of all it should be clear that no right minded historian would claim that some atrocities could possible justify the other or something like that. That is what some denialists and apologists, have tried to do over the years to make propaganda against the Armenian Genocide. This has ultimately resulted in every research of atrocities against Muslims and Turks criticized as apologism or denialism against the Armenian Genocide, and that makes these historical question very discussed and politicized. But beside the fact that Armenian Genocide happened in the hands of the CUP[A] and the Nationalist Movement, at the same time the Muslim and Turk populace were subject to murder and expulsion. Those atrocities can in some context be categorized as Genocide. The Russian forces and Armenians were not as organized in the matter of killing and murder, but atrocities occurred and I will try to give a comprehensive picture of the events against the Muslim populace.

The advancing Russian Army had a clear agenda, the cleansing and expulsion of Muslim populace were a common practice for the Russian Army in the Caucasus(For example. The Cicassian Genocide[1]). When the Russian Army entered eastern Anatolia in 1914, they began a ethnic cleansing against the Muslims in the area. By the end of 1917 the total death toll of Muslims (Mainly Turks and Kurds) were estimated to be around 128.000 to 600.000, many others in the area also died of famine and disease.[2] Those other deaths are often used by apologists and denialists to boost the Muslim deaths, which they argue with saying the same is done by the statistics about Armenian deaths. This again shows their unprofessional and non-objective approach to the matter. The partially religious exodus and mass killings were widely used instrument of war, and It's not in all the cases we have evidence or sources enough prove the intend or planning of Genocide.

The Armenian Irregulars and Rebels are responsible for some 40.000 to 75.000 of these deaths are according to Rudolph J. Rummel, but the main burden here is put on the Russian Forces occupying the area. The Russians were the main authority while they were occupying the area, and the Armenian contingents of the Russian Army were irregulars and volunteers. The atrocities continued after the Russian Army withdraw, and their were power vacuum in the area, the Armenian forces led by General Andranik killed around 10.000 Muslims in Erzincan and Erzurum, and later on burned some 250 Muslim (Tatar and Azerbaijani) in the Kars region.[3].

These atrocities are viewed by some pro-Turkish historians as acts of Genocide, but the fact that it is used to justify the Armenian Genocide makes their research and conclusions questionable. But if we choose look at the events there was a intentional cleansing of a ethno-religious group, with the intend of creating more homogeneous territory. It was is no way as organized and nor widespread as the Ottoman atrocities against the Armenians. Some would argue that the Russian Empire (until 1917) and The First Armenian Republic (between 1918-1920), were responsible for acts of Genocide against the Muslim/Turkish populace in the area.[4] Others would argue that the Armenians were recolonizing their lost homelands, and the acts were a part of the struggles of war.[5] I would conclude that there was atrocities committed Armenian and Russian forces against the Muslim populace, but I have not come across sources that clarifies the act of Genocide. The political intend from unified state entity is missing is this case, compared to the Armenian Genocide. The advancing Russian Army could in some of the cases be held accountable of Genocidal acts, but again the matter of intend and deliberately planning which makes it very difficult to categorize these atrocities as genocide. I personally think that this is a very tangled and politicized matter, and I have a difficult time with the categorizing and definitions since it usually offends some one.

Lastly to summarize the answer, some 128.000-600.000 Muslims were killed by Russian and Armenian forces. I would say they were subject to ethno-religious cleansing. It's a very broadly discussed topic if these killed civilians were victims of Genocide or not, but these death tolls should no way be used to deny or justify the cruel and inhumane atrocities against the Armenians.

References: [1] Richmond, Walter. The Circassian Genocide. Rutgers University Press, 2013.

[2] Rummel, Rudolph J. Statistics of democide: Genocide and mass murder since 1900. Vol. 2. LIT Verlag Münster, 1998. Pages 82-85.

[3] Levene, Mark. Devastation: Volume I: The European Rimlands 1912-1938. Vol. 1. Oxford University Press, 2013. Pages 217-220.

[4] McCarthy, Justin. Death and exile: the ethnic cleansing of Ottoman Muslims, 1821-1922. Princeton, NJ: Darwin Press, 1995. Pages 109-134 and 179-254

[5] Chalabian, Antranig. General Andranik and the Armenian Revolutionary Movement. Antranig Chalabian, 1988.

Glossary: [A] Committee of Union and Progress. Ottoman Turkish Nationalist Party.