diff --git a/dvc/dependency/repo.py b/dvc/dependency/repo.py
index 20439c024e..68cd044a1d 100644
--- a/dvc/dependency/repo.py
+++ b/dvc/dependency/repo.py
@@ -49,10 +49,10 @@ def _make_repo(self, **overrides):
 
     def status(self):
         with self._make_repo() as repo:
-            current = repo.find_out_by_relpath(self.def_path).info
+            current = repo.find_out_by_path(self.def_path).info
 
         with self._make_repo(rev_lock=None) as repo:
-            updated = repo.find_out_by_relpath(self.def_path).info
+            updated = repo.find_out_by_path(self.def_path).info
 
         if current != updated:
             return {str(self): "update available"}
@@ -71,7 +71,7 @@ def fetch(self):
         ) as repo:
             self.def_repo[self.PARAM_REV_LOCK] = repo.scm.get_rev()
 
-            out = repo.find_out_by_relpath(self.def_path)
+            out = repo.find_out_by_path(self.def_path)
             with repo.state:
                 repo.cloud.pull(out.get_used_cache())
 
diff --git a/dvc/exceptions.py b/dvc/exceptions.py
index 3c85f3dae0..369b33ac7f 100644
--- a/dvc/exceptions.py
+++ b/dvc/exceptions.py
@@ -59,10 +59,12 @@ class OutputNotFoundError(DvcException):
         output (unicode): path to the file/directory.
     """
 
-    def __init__(self, output):
+    def __init__(self, output, repo=None):
+        self.repo = repo
+        self.failed_output = output
         super(OutputNotFoundError, self).__init__(
             "unable to find DVC-file with output '{path}'".format(
-                path=relpath(output)
+                path=relpath(self.failed_output)
             )
         )
 
diff --git a/dvc/external_repo.py b/dvc/external_repo.py
index 46657fc4d7..d528af6a55 100644
--- a/dvc/external_repo.py
+++ b/dvc/external_repo.py
@@ -9,6 +9,8 @@
 
 from dvc.config import NoRemoteError
 from dvc.exceptions import RemoteNotSpecifiedInExternalRepoError
+from dvc.exceptions import NoOutputInExternalRepoError
+from dvc.exceptions import OutputNotFoundError
 from dvc.utils.fs import remove
 
 
@@ -25,6 +27,10 @@ def external_repo(url=None, rev=None, rev_lock=None, cache_dir=None):
         yield repo
     except NoRemoteError as exc:
         raise RemoteNotSpecifiedInExternalRepoError(url, cause=exc)
+    except OutputNotFoundError as exc:
+        if exc.repo is repo:
+            raise NoOutputInExternalRepoError(url, exc.failed_output)
+        raise
     repo.close()
 
 
diff --git a/dvc/repo/__init__.py b/dvc/repo/__init__.py
index e0003b8087..86d6a343c7 100644
--- a/dvc/repo/__init__.py
+++ b/dvc/repo/__init__.py
@@ -418,10 +418,13 @@ def stages(self):
         return get_stages(self.graph)
 
     def find_outs_by_path(self, path, outs=None, recursive=False):
+        abs_path = (
+            path if os.path.isabs(path) else os.path.join(self.root_dir, path)
+        )
+
         if not outs:
             outs = [out for stage in self.stages for out in stage.outs]
 
-        abs_path = os.path.abspath(path)
         is_dir = self.tree.isdir(abs_path)
 
         def func(out):
@@ -435,12 +438,15 @@ def func(out):
 
         matched = list(filter(func, outs))
         if not matched:
-            raise OutputNotFoundError(path)
+            if abs_path.startswith(self.root_dir):
+                failed_output = relpath(abs_path)
+            else:
+                failed_output = path
+            raise OutputNotFoundError(failed_output, self)
 
         return matched
 
-    def find_out_by_relpath(self, relpath):
-        path = os.path.join(self.root_dir, relpath)
+    def find_out_by_path(self, path):
         out, = self.find_outs_by_path(path)
         return out
 
diff --git a/dvc/repo/fetch.py b/dvc/repo/fetch.py
index 531fd4d535..0440dddaea 100644
--- a/dvc/repo/fetch.py
+++ b/dvc/repo/fetch.py
@@ -81,7 +81,7 @@ def _fetch_external(self, repo_url, repo_rev, files):
                 cache = NamedCache()
                 for name in files:
                     try:
-                        out = repo.find_out_by_relpath(name)
+                        out = repo.find_out_by_path(name)
                     except OutputNotFoundError:
                         failed += 1
                         logger.exception(
diff --git a/dvc/repo/get.py b/dvc/repo/get.py
index 21d01ed7e7..64ca5eaf07 100644
--- a/dvc/repo/get.py
+++ b/dvc/repo/get.py
@@ -49,7 +49,7 @@ def get(url, path, out=None, rev=None):
             # the same cache file might be used a few times in a directory.
             repo.cache.local.cache_types = ["reflink", "hardlink", "copy"]
 
-            o = repo.find_out_by_relpath(path)
+            o = repo.find_out_by_path(path)
             with repo.state:
                 repo.cloud.pull(o.get_used_cache())
             o.path_info = PathInfo(os.path.abspath(out))
diff --git a/dvc/repo/imp.py b/dvc/repo/imp.py
index 869039266a..68ead389b6 100644
--- a/dvc/repo/imp.py
+++ b/dvc/repo/imp.py
@@ -1,13 +1,6 @@
-from dvc.exceptions import NoOutputInExternalRepoError
-from dvc.exceptions import OutputNotFoundError
-
-
 def imp(self, url, path, out=None, rev=None):
     erepo = {"url": url}
     if rev is not None:
         erepo["rev"] = rev
 
-    try:
-        return self.imp_url(path, out=out, erepo=erepo, locked=True)
-    except OutputNotFoundError:
-        raise NoOutputInExternalRepoError(url, path)
+    return self.imp_url(path, out=out, erepo=erepo, locked=True)