diff --git a/src/intervals/functions.jl b/src/intervals/functions.jl
index 5ea1cf59d..588b163d7 100644
--- a/src/intervals/functions.jl
+++ b/src/intervals/functions.jl
@@ -375,13 +375,18 @@ function nthroot(a::Interval{T}, n::Integer) where T
 end
 
 """
-Calculate `x mod y` where `x` is an interval and `y` is a positive divisor.
+Calculate `x::Interval mod y::Real`, limited by `y != 0`.
 """
 function mod(x::Interval, y::Real)
-    @assert y > zero(y) "modulo is currently implemented only for a positive divisor."
+    @assert y != zero(y) """mod(x::Interval, y::Real) 
+is currently implemented only for a strictly positive or negative divisor y."""
     division = x / y
     fl = floor(division)
-    fl.lo < fl.hi ? Interval(zero(y), y) : y * (division - fl)
+    if !isthin(fl)
+        return y > zero(y) ? Interval(zero(y), y) : Interval(y, zero(y))
+    else
+        return y * (division - fl)
+    end
 end
 
 mod(x:T, y::Interval) where T = throw(ArgumentError("mod not defined for interval as divisor `y`"))
diff --git a/test/interval_tests/numeric.jl b/test/interval_tests/numeric.jl
index 3d88a91a0..d933f9c7c 100644
--- a/test/interval_tests/numeric.jl
+++ b/test/interval_tests/numeric.jl
@@ -446,18 +446,31 @@ end
     @test mod(x, 2) == mod(x, 2.0) ⪆ x
     @test mod(x, 2.5) ⪆ x
     @test mod(x, 0.5) == 0..0.5
+    @test mod(x, -1) == mod(x, -1.0) == -1..0
+    @test mod(x, -2) == mod(x, -2.0) ⪆ -2+x
+    @test mod(x, -2.5) ⪆ -2.5+x
+    @test mod(x, -0.5) == -0.5..0
 
     x = (-1+r) .. -r
     @test mod(x, 1) == mod(x, 1.0) ⪆ 1+x
     @test mod(x, 2) == mod(x, 2.0) ⪆ 2+x
     @test mod(x, 2.5) ⪆ 2.5+x
     @test mod(x, 0.5) == 0..0.5
+    @test mod(x, -1) == mod(x, -1.0) ⪆ x
+    @test mod(x, -2) == mod(x, -2.0) ⪆ x
+    @test mod(x, -2.5) ⪆ x
+    @test mod(x, -0.5) == -0.5..0
 
     x = -r .. 1-r
     @test mod(x, 1) == mod(x, 1.0) == 0..1
     @test mod(x, 2) == mod(x, 2.0) == 0..2
     @test mod(x, 2.5) == 0..2.5
     @test mod(x, 0.5) == 0..0.5
+    @test mod(x, -1) == mod(x, -1.0) == -1..0
+    @test mod(x, -2) == mod(x, -2.0) == -2..0
+    @test mod(x, -2.5) == -2.5..0
+    @test mod(x, -0.5) == -0.5..0
 
-    @test_throws AssertionError mod(x, -1)
+    # TODO - implement mod for two intervals
+    @test_throws TypeError mod(1..2, 1.4..1.5)
 end