A Chronicles of Turkmenistan source in one of the provinces (the name of the velayat is withheld at its request but a similar situation is being observed all across the country) claims that Turkmenistan Airlines does not have any available airline tickets to Moscow until the end of September.
Tickets to Moscow can be purchased in a subsidiary of Russian airlines S7 but in this case only payments in dollars are accepted. The ticket costs $345.
Credit card payments can be made only in Ashgabat but the problem is that a restriction of $50 a day for goods and services applies. In order to transfer the required amount, a prospective passenger needs to find seven relatives willing to help. Additionally, certificates proving family relationship need to be presented at the bank.
The Ashgabat office of S7 Airlines confirmed to Chronicles of Turkmenistan that tickets are available and that payments are accepted in dollars.
Source: Chronicles of Turkmenistan