diff --git a/src/briefcase/platforms/linux/system.py b/src/briefcase/platforms/linux/system.py
index 2adb63cc6..5ac18c19d 100644
--- a/src/briefcase/platforms/linux/system.py
+++ b/src/briefcase/platforms/linux/system.py
@@ -54,16 +54,6 @@ def parse_options(self, extra):
 
         return options
 
-    @property
-    def linux_arch(self):
-        # Linux uses different architecture identifiers for some platforms
-        return {
-            "x86_64": "amd64",
-            "aarch64": "arm64",
-            "armv6l": "armhf",
-            "i686": "i386",
-        }.get(self.tools.host_arch, self.tools.host_arch)
-
     def build_path(self, app):
         # Override the default build path to use the vendor name,
         # rather than "linux"
@@ -86,31 +76,6 @@ def rpm_tag(self, app):
         else:
             return f"el{app.target_codename}"
 
-    def distribution_filename(self, app):
-        if app.packaging_format == "deb":
-            return (
-                f"{app.app_name}_{app.version}-{getattr(app, 'revision', 1)}"
-                f"~{app.target_vendor}-{app.target_codename}_{self.linux_arch}.deb"
-            )
-        elif app.packaging_format == "rpm":
-            return (
-                f"{app.app_name}-{app.version}-{getattr(app, 'revision', 1)}"
-                f".{self.rpm_tag(app)}.{self.tools.host_arch}.rpm"
-            )
-        elif app.packaging_format == "pkg":
-            return (
-                f"{app.app_name}-{app.version}-{getattr(app, 'revision', 1)}"
-                f"-{self.tools.host_arch}.pkg.tar.zst"
-            )
-        else:
-            raise BriefcaseCommandError(
-                "Briefcase doesn't currently know how to build system packages in "
-                f"{app.packaging_format.upper()} format."
-            )
-
-    def distribution_path(self, app):
-        return self.dist_path / self.distribution_filename(app)
-
     def target_glibc_version(self, app):
         target_glibc = self.tools.os.confstr("CS_GNU_LIBC_VERSION").split()[1]
         return target_glibc
@@ -248,6 +213,62 @@ def app_python_version_tag(self, app):
             python_version_tag = super().app_python_version_tag(app)
         return python_version_tag
 
+    def deb_abi(self, app: AppConfig):
+        try:
+            return self._deb_abi
+        except AttributeError:
+            self._deb_abi = (
+                self.tools[app]
+                .app_context.check_output(["dpkg", "--print-architecture"])
+                .strip()
+            )
+            return self._deb_abi
+
+    def rpm_abi(self, app: AppConfig):
+        try:
+            return self._rpm_abi
+        except AttributeError:
+            self._rpm_abi = (
+                self.tools[app]
+                .app_context.check_output(["rpm", "--eval", "%_target_cpu"])
+                .strip()
+            )
+            return self._rpm_abi
+
+    def pkg_abi(self, app: AppConfig):
+        try:
+            return self._pkg_abi
+        except AttributeError:
+            self._pkg_abi = (
+                self.tools[app].app_context.check_output(["uname", "-m"]).strip()
+            )
+            return self._pkg_abi
+
+    def distribution_filename(self, app):
+        if app.packaging_format == "deb":
+            return (
+                f"{app.app_name}_{app.version}-{getattr(app, 'revision', 1)}"
+                f"~{app.target_vendor}-{app.target_codename}_{self.deb_abi(app)}.deb"
+            )
+        elif app.packaging_format == "rpm":
+            return (
+                f"{app.app_name}-{app.version}-{getattr(app, 'revision', 1)}"
+                f".{self.rpm_tag(app)}.{self.rpm_abi(app)}.rpm"
+            )
+        elif app.packaging_format == "pkg":
+            return (
+                f"{app.app_name}-{app.version}-{getattr(app, 'revision', 1)}"
+                f"-{self.pkg_abi(app)}.pkg.tar.zst"
+            )
+        else:
+            raise BriefcaseCommandError(
+                "Briefcase doesn't currently know how to build system packages in "
+                f"{app.packaging_format.upper()} format."
+            )
+
+    def distribution_path(self, app):
+        return self.dist_path / self.distribution_filename(app)
+
     def target_glibc_version(self, app):
         """Determine the glibc version.
 
@@ -879,15 +900,15 @@ def _package_deb(self, app: AppConfig, **kwargs):
                 f.write(
                     "\n".join(
                         [
-                            f"Package: { app.app_name }",
-                            f"Version: { app.version }",
-                            f"Architecture: { self.linux_arch }",
-                            f"Maintainer: { app.author } <{ app.author_email }>",
-                            f"Homepage: { app.url }",
-                            f"Description: { app.description }",
-                            f" { debian_multiline_description(app.long_description) }",
-                            f"Depends: { system_runtime_requires }",
-                            f"Section: { getattr(app, 'system_section', 'utils') }",
+                            f"Package: {app.app_name}",
+                            f"Version: {app.version}",
+                            f"Architecture: {self.deb_abi(app)}",
+                            f"Maintainer: {app.author } <{app.author_email}>",
+                            f"Homepage: {app.url}",
+                            f"Description: {app.description}",
+                            f" {debian_multiline_description(app.long_description)}",
+                            f"Depends: {system_runtime_requires}",
+                            f"Section: {getattr(app, 'system_section', 'utils')}",
                             "Priority: optional\n",
                         ]
                     )
@@ -993,7 +1014,7 @@ def _package_rpm(self, app: AppConfig, **kwargs):  # pragma: no-cover-if-is-wind
                         ]
                         + [
                             "",
-                            f"ExclusiveArch:  {self.tools.host_arch}",
+                            f"ExclusiveArch:  {self.rpm_abi(app)}",
                             "",
                             "%description",
                             app.long_description,
@@ -1071,7 +1092,7 @@ def _package_rpm(self, app: AppConfig, **kwargs):  # pragma: no-cover-if-is-wind
         self.tools.shutil.move(
             rpmbuild_path
             / "RPMS"
-            / self.tools.host_arch
+            / self.rpm_abi(app)
             / self.distribution_filename(app),
             self.distribution_path(app),
         )
@@ -1139,7 +1160,7 @@ def _package_pkg(self, app: AppConfig, **kwargs):  # pragma: no-cover-if-is-wind
                             f"pkgver={app.version}",
                             f"pkgrel={getattr(app, 'revision', 1)}",
                             f'pkgdesc="{app.description}"',
-                            f"arch=('{self.tools.host_arch}')",
+                            f"arch=('{self.pkg_abi(app)}')",
                             f'url="{app.url}"',
                             f"license=('{app.license}')",
                             f"depends=({system_runtime_requires})",