Later, she grumbled about "despicable parasites" criticising her on Twitter: "Were you ordered by your employers to respond to me in unison and with the same predetermined script? Be creative."
Cuba accuses dissidents like Sanchez of being mercenaries in the hire of Washington.
Their exchange is unlikely to be noticed by many in Cuba, where the decades-old US economic embargo has left the island without a hardwired internet connection to the rest of the world.
Cuba relies on plodding, expensive satellite service and Internet access is rare and costly, though hopes for faster service arrived earlier this year along with an undersea fiber-optic cable from Venezuela.
Authorities previously said the cable could be operational as early as July, but there has been no official word since and no noticeable improvement in Internet speeds.