Blinken criticized FIFA for threatening to punish World Cup players who wear a "One Love" armband.
"As national federations, we can't put our players in a position where they could face sporting sanctions including bookings, so we have asked the captains not to attempt to wear the armbands in FIFA World Cup games."
The nations decried the FIFA decision as "unprecedented" and said they were "very frustrated."
Fans wearing clothing featuring rainbows, a symbol of support for the LGBTQ community, have reported being prevented from entering World Cup stadiums in Qatar.
FIFA, soccer's global governing body, previously said fans were "welcome to express themselves; they are welcome to express their love for their partners."