A search for the decays
B
0
s
→
e
+
e
−
and
B
0
→
e
+
e
−
is performed using data collected with the LHCb experiment in proton-proton collisions at center-of-mass energies of 7, 8, and 13 TeV, corresponding to integrated luminosities of 1, 2, and
2
 
 
fb
−
1
, respectively. No signal is observed. Assuming no contribution from
B
0
→
e
+
e
−
decays, an upper limit on the branching fraction
B
(
B
0
s
→
e
+
e
−
)
<
9.4
(
11.2
)
×
10
−
9
is obtained at 90(95)% confidence level. If no
B
0
s
→
e
+
e
−
contribution is assumed, a limit of
B
(
B
0
→
e
+
e
−
)
<
2.5
(
3.0
)
×
10
−
9
is determined at 90(95)% confidence level. These upper limits are more than one order of magnitude lower than the previous values.