I checked the Wikipedia article on the topic of the purges and I see that the Obama administration, as well some EU & European national governments' officials have expressed various levels of concern. The Wikipedia article look pretty scanty though. (I seem to recall the EU reactions were more voluminous and more colorful than the couple mentioned there.) It [also] doesn't say anything about Trump's administration's position on the matter. So, has there been any official position of the Trump administration on the Turkish purges? Did the Trump officials (or Trump himself) at least comment unofficially about the purges? Clearly the matter is still of some present-day relevance, Reuters reported for instace a purge of 18,000 this mounth.
According to State Department press briefings and statements, the Trump administration fully supports the Turkish government, but has concerns over the abuse of emergency powers to ignore Turkish and US citizens' constitutional rights.
Two years ago, nearly 250 Turkish citizens lost their lives, and thousands were wounded in the heinous failed coup attempt of July 15. We offer our deepest condolences to the friends and loved ones of those injured or killed. The failed coup attempt was an attack on democracy and a stark reminder that the preservation of democracy requires perseverance and safeguards for fundamental freedoms. We reaffirm the United States’ steadfast support for our NATO Ally Turkey and its democratic institutions.
Clearly, the administration supports the Turkish government. However, they definitely have concerns over the government's abuse of power in order to perform the purges. From this press briefing on May 3rd, in response to a question about free press in Turkey:
MS NAUERT: Yeah. I think our position on the importance of a free press is very well known... You’re absolutely right, there are more journalists jailed in Turkey than in any other country around the world. That is a tremendous concern. We believe that more voices rather than fewer voices being heard helps advance a democratic society and helps give people voice to their concerns.
We support the goal of improved media freedom in Turkey; we’ve discussed that a lot here at the State Department. We raise the issue – I want to tell you – directly with the Turkish Government on many occasions.
And this press briefing from :
MS NAUERT: ... will continue to follow his case closely along with those of other U.S. citizens whose ongoing prosecution under the state of emergency raises serious concerns about respect for judicial independence, protections enshrined in the Turkish constitution, including an individual’s right to a fair trial.
We’d like to call on the Turkish Government to end the protracted state of emergency, to release those detained arbitrarily under emergency authorities, and to safeguard the rule of law consistent with Turkey’s own domestic and international obligations and commitments.
In short, the administration is certainly expressing concern over the abuse of emergency powers in regards to the purges, but whether or not that is 'condemning' them is more a matter of opinion.