diff --git a/cwltool/singularity.py b/cwltool/singularity.py
index 0029d3950..40d1bc9b5 100644
--- a/cwltool/singularity.py
+++ b/cwltool/singularity.py
@@ -75,6 +75,14 @@ def is_apptainer_1_or_newer() -> bool:
     return v[0][0] >= 1
 
 
+def is_apptainer_1_1_or_newer() -> bool:
+    """Check if apptainer singularity distribution is version 1.1 or higher."""
+    v = get_version()
+    if v[1] != "apptainer":
+        return False
+    return v[0][0] >= 2 or (v[0][0] >= 1 and v[0][1] >= 1)
+
+
 def is_version_2_6() -> bool:
     """
     Check if this singularity version is exactly version 2.6.
@@ -119,6 +127,12 @@ def is_version_3_9_or_newer() -> bool:
     return v[0][0] >= 4 or (v[0][0] == 3 and v[0][1] >= 9)
 
 
+def is_version_3_10_or_newer() -> bool:
+    """Detect if Singularity v3.10+ is available."""
+    v = get_version()
+    return v[0][0] >= 4 or (v[0][0] == 3 and v[0][1] >= 10)
+
+
 def _normalize_image_id(string: str) -> str:
     return string.replace("/", "_") + ".img"
 
@@ -464,14 +478,18 @@ def create_runtime(
     ) -> tuple[list[str], Optional[str]]:
         """Return the Singularity runtime list of commands and options."""
         any_path_okay = self.builder.get_requirement("DockerRequirement")[1] or False
+
         runtime = [
             "singularity",
             "--quiet",
-            "exec",
+            "run" if is_apptainer_1_1_or_newer() or is_version_3_10_or_newer() else "exec",
             "--contain",
             "--ipc",
             "--cleanenv",
         ]
+        if is_apptainer_1_1_or_newer() or is_version_3_10_or_newer():
+            runtime.append("--no-eval")
+
         if singularity_supports_userns():
             runtime.append("--userns")
         else:
diff --git a/tests/test_environment.py b/tests/test_environment.py
index a4bfd1ac3..488477aa7 100644
--- a/tests/test_environment.py
+++ b/tests/test_environment.py
@@ -159,6 +159,9 @@ def BIND(v: str, env: Env) -> bool:
                         return v.startswith(tmp_prefix) and v.endswith(":/tmp")
 
                     sing_vars["SINGULARITY_BIND"] = BIND
+        if vminor >= 10:
+            sing_vars["SINGULARITY_COMMAND"] = "run"
+            sing_vars["SINGULARITY_NO_EVAL"] = None
 
         result.update(sing_vars)