diff --git a/examples/python/funcs.py b/examples/python/funcs.py
index 2f4830676e..f38aca53f2 100644
--- a/examples/python/funcs.py
+++ b/examples/python/funcs.py
@@ -1,9 +1,10 @@
 # Python function that implements a loop of short runs
 # calls back to LAMMPS via "lmp" instance
 # lammps() must be called with ptr=lmpptr for this to work
+from __future__ import print_function
 
 def loop(N,cut0,thresh,lmpptr):
-  print "LOOP ARGS",N,cut0,thresh,lmpptr
+  print("LOOP ARGS",N,cut0,thresh,lmpptr)
   from lammps import lammps
   lmp = lammps(ptr=lmpptr)
   natoms = lmp.get_natoms()
@@ -12,11 +13,12 @@ def loop(N,cut0,thresh,lmpptr):
     cut = cut0 + i*0.1
 
     lmp.set_variable("cut",cut)                 # set a variable in LAMMPS
+
     lmp.command("pair_style lj/cut ${cut}")     # LAMMPS command
     #lmp.command("pair_style lj/cut %d" % cut)  # LAMMPS command option
 
     lmp.command("pair_coeff * * 1.0 1.0")       # ditto
     lmp.command("run 10")                       # ditto
     pe = lmp.extract_compute("thermo_pe",0,0)   # extract total PE from LAMMPS
-    print "PE",pe/natoms,thresh
+    print("PE",pe/natoms,thresh)
     if pe/natoms < thresh: return
diff --git a/examples/python/in.python b/examples/python/in.python
index cb2013fdd3..c5aa504d43 100644
--- a/examples/python/in.python
+++ b/examples/python/in.python
@@ -25,13 +25,14 @@ run		10
 # example of catching a syntax error
 
 python          simple here """
+from __future__ import print_function
+
 def simple():
-  import exceptions
-  print "Inside simple function"
+  print("Inside simple function")
   try:
     foo += 1
-  except Exception, e:
-    print "FOO error:",e
+  except Exception as e:
+    print("FOO error:", e)
 """
 
 python          simple invoke
diff --git a/lib/python/Makefile.lammps.python3 b/lib/python/Makefile.lammps.python3
new file mode 100644
index 0000000000..1d5d5f2d81
--- /dev/null
+++ b/lib/python/Makefile.lammps.python3
@@ -0,0 +1,6 @@
+# Settings that the LAMMPS build will import when this package library is used
+# See the README file for more explanation
+
+python_SYSINC = $(shell which python3-config > /dev/null 2>&1 && python3-config --includes || python-config --includes )
+python_SYSLIB = $(shell which python3-config > /dev/null 2>&1 && python3-config --ldflags || python-config --ldflags)
+python_SYSPATH =
diff --git a/lib/python/README b/lib/python/README
index ddccc1a21a..077c2547d2 100644
--- a/lib/python/README
+++ b/lib/python/README
@@ -6,10 +6,6 @@ and your version of Python, and copy it to Makefile.lammps before
 building LAMMPS itself.  You may need to edit one of the provided
 files to match your system.
 
-Note that is not currently possible to use the PYTHON package with
-Python 3, only with Python 2.  The C API changed from Python 2 to 3
-and the LAMMPS code is not compatible with both.
-
 If you create a new Makefile.lammps file suitable for some version of
 Python on some system, that is not a match to one of the provided
 Makefile.lammps.* files, you can send it to the developers, and we can
diff --git a/python/lammps.py b/python/lammps.py
index a36abb87e8..d428a097a8 100644
--- a/python/lammps.py
+++ b/python/lammps.py
@@ -30,7 +30,7 @@ from collections import namedtuple
 import os
 import select
 import re
-
+import sys
 
 class MPIAbortException(Exception):
   def __init__(self, message):
@@ -151,9 +151,16 @@ class lammps(object):
 
     else:
       # magic to convert ptr to ctypes ptr
-      pythonapi.PyCObject_AsVoidPtr.restype = c_void_p
-      pythonapi.PyCObject_AsVoidPtr.argtypes = [py_object]
-      self.lmp = c_void_p(pythonapi.PyCObject_AsVoidPtr(ptr))
+      if sys.version_info >= (3, 0):
+        # Python 3 (uses PyCapsule API)
+        pythonapi.PyCapsule_GetPointer.restype = c_void_p
+        pythonapi.PyCapsule_GetPointer.argtypes = [py_object, c_char_p]
+        self.lmp = c_void_p(pythonapi.PyCapsule_GetPointer(ptr, None))
+      else:
+        # Python 2 (uses PyCObject API)
+        pythonapi.PyCObject_AsVoidPtr.restype = c_void_p
+        pythonapi.PyCObject_AsVoidPtr.argtypes = [py_object]
+        self.lmp = c_void_p(pythonapi.PyCObject_AsVoidPtr(ptr))
 
   def __del__(self):
     if self.lmp and self.opened:
@@ -305,7 +312,7 @@ class lammps(object):
   def set_variable(self,name,value):
     if name: name = name.encode()
     if value: value = str(value).encode()
-    return self.lib.lammps_set_variable(self.lmp,name,str(value))
+    return self.lib.lammps_set_variable(self.lmp,name,value)
 
   # return current value of thermo keyword
 
diff --git a/src/PYTHON/python.cpp b/src/PYTHON/python.cpp
index 74591c1c16..c465086f63 100644
--- a/src/PYTHON/python.cpp
+++ b/src/PYTHON/python.cpp
@@ -25,6 +25,22 @@ enum{NONE,INT,DOUBLE,STRING,PTR};
 
 #define VALUELENGTH 64               // also in variable.cpp
 
+// Wrap API changes between Python 2 and 3 using macros
+#if PY_MAJOR_VERSION == 2
+#define PY_INT_FROM_LONG(X) PyInt_FromLong(X)
+#define PY_INT_AS_LONG(X) PyInt_AsLong(X)
+#define PY_STRING_FROM_STRING(X) PyString_FromString(X)
+#define PY_VOID_POINTER(X) PyCObject_FromVoidPtr((void *) X, NULL)
+#define PY_STRING_AS_STRING(X) PyString_AsString(X)
+
+#elif PY_MAJOR_VERSION == 3
+#define PY_INT_FROM_LONG(X) PyLong_FromLong(X)
+#define PY_INT_AS_LONG(X) PyLong_AsLong(X)
+#define PY_STRING_FROM_STRING(X) PyUnicode_FromString(X)
+#define PY_VOID_POINTER(X) PyCapsule_New((void *) X, NULL, NULL)
+#define PY_STRING_AS_STRING(X) PyUnicode_AsUTF8(X)
+#endif
+
 /* ---------------------------------------------------------------------- */
 
 Python::Python(LAMMPS *lmp) : Pointers(lmp)
@@ -257,8 +273,10 @@ void Python::invoke_function(int ifunc, char *result)
           error->all(FLERR,"Could not evaluate Python function input variable");
         }
 
-        pValue = PyInt_FromLong(atoi(str));
-      } else pValue = PyInt_FromLong(pfuncs[ifunc].ivalue[i]);
+        pValue = PY_INT_FROM_LONG(atoi(str));
+      } else {
+        pValue = PY_INT_FROM_LONG(pfuncs[ifunc].ivalue[i]);
+      }
     } else if (itype == DOUBLE) {
       if (pfuncs[ifunc].ivarflag[i]) {
         str = input->variable->retrieve(pfuncs[ifunc].svalue[i]);
@@ -269,7 +287,9 @@ void Python::invoke_function(int ifunc, char *result)
         }
 
         pValue = PyFloat_FromDouble(atof(str));
-      } else pValue = PyFloat_FromDouble(pfuncs[ifunc].dvalue[i]);
+      } else {
+        pValue = PyFloat_FromDouble(pfuncs[ifunc].dvalue[i]);
+      }
     } else if (itype == STRING) {
       if (pfuncs[ifunc].ivarflag[i]) {
         str = input->variable->retrieve(pfuncs[ifunc].svalue[i]);
@@ -277,10 +297,13 @@ void Python::invoke_function(int ifunc, char *result)
           PyGILState_Release(gstate);
           error->all(FLERR,"Could not evaluate Python function input variable");
         }
-        pValue = PyString_FromString(str);
-      } else pValue = PyString_FromString(pfuncs[ifunc].svalue[i]);
+
+        pValue = PY_STRING_FROM_STRING(str);
+      } else {
+        pValue = PY_STRING_FROM_STRING(pfuncs[ifunc].svalue[i]);
+      }
     } else if (itype == PTR) {
-      pValue = PyCObject_FromVoidPtr((void *) lmp,NULL);
+      pValue = PY_VOID_POINTER(lmp);
     }
     PyTuple_SetItem(pArgs,i,pValue);
   }
@@ -304,11 +327,11 @@ void Python::invoke_function(int ifunc, char *result)
   if (pfuncs[ifunc].noutput) {
     int otype = pfuncs[ifunc].otype;
     if (otype == INT) {
-      sprintf(result,"%ld",PyInt_AsLong(pValue));
+      sprintf(result,"%ld",PY_INT_AS_LONG(pValue));
     } else if (otype == DOUBLE) {
       sprintf(result,"%.15g",PyFloat_AsDouble(pValue));
     } else if (otype == STRING) {
-      char *pystr = PyString_AsString(pValue);
+      char *pystr = PY_STRING_AS_STRING(pValue);
       if (pfuncs[ifunc].longstr) 
         strncpy(pfuncs[ifunc].longstr,pystr,pfuncs[ifunc].length_longstr);
       else strncpy(result,pystr,VALUELENGTH-1);