It's unclear.

Let me explain this by first saying a few words on the available scholarship: Despite the integration of homosexuals, specifically gay men, as one of the main groups of victims of the Nazis in the public consciousness since the 70s and 80s, which I discuss in this answer, there is still a distinct lack in academic monographs on the subject that provide an in-depth overview, especially in English. Burkhard Jellonek has delivered the only comprehensive German language monograph with Homosexuelle unter dem Hakenkreuz in 1990 while the 1986 monograph by Richard Plant The Pink Triangle is not an academic monograph but more of an overview written by someone who was himself a victim of anti-homosexual and anti-Jewish persecution. Also, a look at the bibliography on the persecution of homosexuals collected by the USHMM further demonstrates this problem. As you can see, the English language literature mentioned as part of this bibliography consists mostly of articles rather than in-depth monographs and what is listed concerns mostly Germany. F.ex. Grau, Günter. Hidden Holocaust?: Gay and Lesbian Persecution in Germany, 1933-45 is a collection of primary documents rather than an overarching treatment while Lautmann, Rudiger, Erhard Vismar, and Jack Nusan Porter. Sexual Politics in the Third Reich: The Persecution of the Homosexuals During the Holocaust. is the only comprehensive English work on the subject and that was published almost 20 years ago.

The one fundamental problem concerning this subject is the same we encounter for virtually every victim group outside of political prisoners and Jews, especially concerning those who faced additional discrimination after the war. There is incredibly little known about the group of homosexuals persecuted by the Nazis because the ongoing stigmatization and discrimination after the war prevented a sort of canon of commemorative literature and first person accounts to emerge. Additionally, it is important to emphasize, as I describe in this answer, a large portion of homosexuals persecuted by the Nazis were not imprisoned in the camps as prisoners with a pink triangle but with a green one, meaning as criminals. Their imprisonment in the camps was justified by the Nazis because they saw them as "repeat offenders", meaning people who had been sentenced by the courts several times for homosexual acts or because the Nazis saw them as "preventive prisoners", meaning that they thought them likely to commit their "crime" again.

Dagmar Lieske in her book Unbequeme Opfer was able to identify about 9000 prisoners of Sachsenhausen who were classified with a green triangle, meaning both "professional criminals" and "preventive prisoners". Of those, more than a thousand were imprisoned because of sexual crimes, in the vast majority, meaning repeated convictions because of homosexual activity (about 800 of all, about 200 were mainly pimps and prostitutes with repeat convictions, and 53 people sentenced because of other sexual crimes). This goes to show that the prosecution of homosexuals and criminals by the Nazis were very much intertwined and both are subjects where we have comparatively little information, especially for the occupied and controlled territories.

The problem with the occupied and controlled territories is that in territories where no "native" state or administration existed (in the General Government and the Soviet Union) as opposed to f.ex. France, Belgium or the Netherlands, sources on the subject of criminal prosecution, especially that directly managed by the Gestapo have either been destroyed or are strewn over a massive amount of small local archives in what was for a very long time the Eastern Bloc. We know a lot about the persecution of Jews because of the centralized character of that form of persecution, various forms of decentralized persecution such as that of the homosexuals are simply less well documented because of these facts.

What we can establish is that for territories like France, Belgium and the Netherlands, the persecution or not persecution was left largely to these native administrations. Vichy France f.ex. introduced legislation prohibiting homosexuality under the age of 21 with the consequence being a fine or six months to three years in prison – which while still dehumanizing and unacceptable was also a far cry from indefinite detention in Nazi concentration camps.

As mentioned above, in territories directly controlled by the Nazis such as the General Government in Poland or the territory of the Soviet Union occupied by the Nazis, the situation is less clear. Concerning the General Government there is a couple of documents that suggest a very mixed approach: In January 1941 Roland Freisler, State Secretary of the Reich Ministry of Justice, and President of the so-called People's Court, authored a memo on the judicial prosecution of homosexuals in the GG stating that it represented "no endangerment of German racial interests [...] when Poles commit homosexual acts among themselves.", leading him to call for more lenient punishments as long as no Germans were involved. However, in the summer of 1942, Martin Bromann informed the Justice Ministry that this policy was not to continue further and that Ernst Kaltenbrunner, head of the Reich Security Main Office, was drafting a directive to deport homosexual Poles to remote areas in Poland so that they would be as isolated as possible from the general population. What became of this directive is unknown and so far, no evidence has been unearthed of a concerted, systematic effort to institute this or any other systematic policy against homosexuals in Poland. What individual Gestapo offices and other units in control of Polish territory did when they came across homosexuals however is another matter that also remains unclear to this day.

There are pieces of evidence showing that at least some courts and police agencies were concerned with persecuting homosexuals outside of Reich territory such as one case from Albania under German occupation and a court case in Budapest dated January 31, 1945 but not enough to paint a comprehensive picture.

Concerning the Soviet Union, there is also very little out there in terms of scholarship. In the Soviet case, there still is very much to uncover. Martin Holler has only recently uncovered a lot of details on the persecution and murder of Roma and Sinti in the Soviet Union, the question whether there was a systematic campaign to murder mentally and physically handicapped people in the USSR remains still unanswered, and the question of the persecution of homosexuals has so far not been dealt with at all to my knowledge (/u/kieslowskifan might know more?) when it comes to policy in the USSR. This is also most likely not going to change for the foreseeable future since the "golden age" of access to Soviet/Russian archives has ended recently with the Putin government becoming more and more restrictive concerning access for Western scholars.

In this sense and in summary: The answer to your question is at the moment unclear. No evidence has so far surfaced that there was a program of persecution of homosexuals comparable to that in the Reich while few documents point to individual agencies or institutions still persecuting homosexuals outside of the Reich.