Icelandair has round-trip flights from Denver (DEN) to Istanbul (IST) for $543-$550 with a connection. Flights in September. Departures on Saturday. Origin/Destination reversible.
Some small OTAs on Skyscanner have this for as low as $526; which is cheaper than the airline. If you plan on booking there, beware of any site that charges a fee to cancel a ticket within the 24-hour “free” period. Use unknown booking sites at your own risk.
This fare has a long 6-hour layover in Reykjavik Iceland (KEF), but I think the discount makes it worth the airport wait time.