An element
g
g
of a group
G
G
is said to be right Engel if for every
x
∈
G
x\in G
there is a number
n
=
n
(
g
,
x
)
n=n(g,x)
such that
[
g
,
n
x
]
=
1
[g,{}_{n}x]=1
. We prove that if a profinite group
G
G
admits a coprime automorphism
φ
\varphi
of prime order such that every fixed point of
φ
\varphi
is a right Engel element, then
G
G
is locally nilpotent.