diff --git a/ext/openssl/ossl_ssl.c b/ext/openssl/ossl_ssl.c
index b3f15f0e..1c93d99a 100644
--- a/ext/openssl/ossl_ssl.c
+++ b/ext/openssl/ossl_ssl.c
@@ -1916,7 +1916,7 @@ ossl_ssl_read_internal(int argc, VALUE *argv, VALUE self, int nonblock)
 {
     SSL *ssl;
     int ilen;
-    VALUE len, str;
+    VALUE len, str, cb_state;
     VALUE opts = Qnil;
 
     if (nonblock) {
@@ -1949,6 +1949,14 @@ ossl_ssl_read_internal(int argc, VALUE *argv, VALUE self, int nonblock)
     rb_str_locktmp(str);
     for (;;) {
         int nread = SSL_read(ssl, RSTRING_PTR(str), ilen);
+
+        cb_state = rb_attr_get(self, ID_callback_state);
+        if (!NIL_P(cb_state)) {
+            rb_ivar_set(self, ID_callback_state, Qnil);
+            ossl_clear_error();
+            rb_jump_tag(NUM2INT(cb_state));
+        }
+
         switch (ssl_get_error(ssl, nread)) {
           case SSL_ERROR_NONE:
             rb_str_unlocktmp(str);
@@ -2038,7 +2046,7 @@ ossl_ssl_write_internal(VALUE self, VALUE str, VALUE opts)
     SSL *ssl;
     rb_io_t *fptr;
     int num, nonblock = opts != Qfalse;
-    VALUE tmp;
+    VALUE tmp, cb_state;
 
     GetSSL(self, ssl);
     if (!ssl_started(ssl))
@@ -2055,6 +2063,14 @@ ossl_ssl_write_internal(VALUE self, VALUE str, VALUE opts)
 
     for (;;) {
         int nwritten = SSL_write(ssl, RSTRING_PTR(tmp), num);
+
+        cb_state = rb_attr_get(self, ID_callback_state);
+        if (!NIL_P(cb_state)) {
+            rb_ivar_set(self, ID_callback_state, Qnil);
+            ossl_clear_error();
+            rb_jump_tag(NUM2INT(cb_state));
+        }
+
         switch (ssl_get_error(ssl, nwritten)) {
           case SSL_ERROR_NONE:
             return INT2NUM(nwritten);
diff --git a/test/openssl/test_ssl_session.rb b/test/openssl/test_ssl_session.rb
index 89cf672a..d9b49a20 100644
--- a/test/openssl/test_ssl_session.rb
+++ b/test/openssl/test_ssl_session.rb
@@ -219,11 +219,11 @@ def test_server_session_cache
   # deadlock.
   TEST_SESSION_REMOVE_CB = ENV["OSSL_TEST_ALL"] == "1"
 
-  def test_ctx_client_session_cb
-    ctx_proc = proc { |ctx| ctx.ssl_version = :TLSv1_2 }
-    start_server(ctx_proc: ctx_proc) do |port|
+  def test_ctx_client_session_cb_tls12
+    start_server do |port|
       called = {}
       ctx = OpenSSL::SSL::SSLContext.new
+      ctx.min_version = ctx.max_version = :TLS1_2
       ctx.session_cache_mode = OpenSSL::SSL::SSLContext::SESSION_CACHE_CLIENT
       ctx.session_new_cb = lambda { |ary|
         sock, sess = ary
@@ -233,7 +233,6 @@ def test_ctx_client_session_cb
         ctx.session_remove_cb = lambda { |ary|
           ctx, sess = ary
           called[:remove] = [ctx, sess]
-          # any resulting value is OK (ignored)
         }
       end
 
@@ -241,8 +240,8 @@ def test_ctx_client_session_cb
         assert_equal(1, ctx.session_cache_stats[:cache_num])
         assert_equal(1, ctx.session_cache_stats[:connect_good])
         assert_equal([ssl, ssl.session], called[:new])
-        assert(ctx.session_remove(ssl.session))
-        assert(!ctx.session_remove(ssl.session))
+        assert_equal(true, ctx.session_remove(ssl.session))
+        assert_equal(false, ctx.session_remove(ssl.session))
         if TEST_SESSION_REMOVE_CB
           assert_equal([ctx, ssl.session], called[:remove])
         end
@@ -250,6 +249,50 @@ def test_ctx_client_session_cb
     end
   end
 
+  def test_ctx_client_session_cb_tls13
+    omit "TLS 1.3 not supported" unless tls13_supported?
+    omit "LibreSSL does not call session_new_cb in TLS 1.3" if libressl?
+
+    start_server do |port|
+      called = {}
+      ctx = OpenSSL::SSL::SSLContext.new
+      ctx.min_version = :TLS1_3
+      ctx.session_cache_mode = OpenSSL::SSL::SSLContext::SESSION_CACHE_CLIENT
+      ctx.session_new_cb = lambda { |ary|
+        sock, sess = ary
+        called[:new] = [sock, sess]
+      }
+
+      server_connect_with_session(port, ctx, nil) { |ssl|
+        ssl.puts("abc"); assert_equal("abc\n", ssl.gets)
+
+        assert_operator(1, :<=, ctx.session_cache_stats[:cache_num])
+        assert_operator(1, :<=, ctx.session_cache_stats[:connect_good])
+        assert_equal([ssl, ssl.session], called[:new])
+      }
+    end
+  end
+
+  def test_ctx_client_session_cb_tls13_exception
+    omit "TLS 1.3 not supported" unless tls13_supported?
+    omit "LibreSSL does not call session_new_cb in TLS 1.3" if libressl?
+
+    start_server do |port|
+      ctx = OpenSSL::SSL::SSLContext.new
+      ctx.min_version = :TLS1_3
+      ctx.session_cache_mode = OpenSSL::SSL::SSLContext::SESSION_CACHE_CLIENT
+      ctx.session_new_cb = lambda { |ary|
+        raise "in session_new_cb"
+      }
+
+      server_connect_with_session(port, ctx, nil) { |ssl|
+        assert_raise_with_message(RuntimeError, /in session_new_cb/) {
+          ssl.puts("abc"); assert_equal("abc\n", ssl.gets)
+        }
+      }
+    end
+  end
+
   def test_ctx_server_session_cb
     connections = nil
     called = {}