We studied magnetostatic response of the Bi
0.9
La
0.1
FeO
3
– KBr composites (BLFO-KBr) consisting of nanosized (≈100 nm) ferrite Bi
0.9
La
0.1
FeO
3
(BLFO) conjugated with fine grinded ionic conducting KBr. When the fraction of KBr is rather small (less than 15 wt%) the magnetic response of the composite is very weak and similar to that observed for the BLFO (pure KBr matrix without Bi
1-x
La
x
FeO
3
has no magnetic response as anticipated). However, when the fraction of KBr increases above 15%, the magnetic response of the composite changes substantially and the field dependence of magnetization reveals ferromagnetic-like hysteresis loop with a remanent magnetization about 0.14 emu/g and coercive field about 1.8 Tesla (at room temperature). Nothing similar to the ferromagnetic-like hysteresis loop can be observed in Bi
1-z
La
z
FeO
3
ceramics with z ≤ 0.15, which magnetization quasi-linearly increases with magnetic field. Different physical mechanisms were considered to explain the unusual experimental results for BLFO-KBr nanocomposites, but only those among them, which are highly sensitive to the interaction of antiferromagnetic Bi
0.9
La
0.1
FeO
3
with ionic conductor KBr, can be relevant.