How to rotate object slowly on only Z axis

I know from experience answering rotation questions, that my interpretation of the question is sometimes different that your intent. Here is an implementation of what I think you are asking:

 var target: Transform;
 var speed: float = 25.0;
 
 function Update () {    
     var step = speed * Time.deltaTime;
     
     var v3 = target.right - (Vector3.Dot(target.right, transform.forward) * transform.forward);
     var q = Quaternion.FromToRotation(transform.right, v3);
     transform.rotation = Quaternion.RotateTowards(transform.rotation, q, step);
     transform.position = Vector3.MoveTowards(transform.position, target.position, step);
 }

It works by taking the transform.right of the target and projecting it on to the XY plane of object containing this script. It then rotates to match its Transform.right vector with the vector projected on to the plane.

This is just code that is a response to a comment, it is not an answer, the code wouldn't fit in a comment box.

 // Move by tapping on the ground in the scenery or with the joystick in the lower left corner.
 // Look around by dragging the screen.
  
 // These controls are a simple version of the navigation controls in Epic's Epic Citadel demo.
  
 // The ground object  must be on the layer 8 (I call it Ground layer).
  
 // Attach this script to a character controller game object. That game object must
 // also have a child object with the main camera attached to it.
  
  
 using UnityEngine;
 using System.Collections;
  
  
  
 [RequireComponent (typeof (CharacterController))]
 public class EpicCitadelControl : MonoBehaviour {
  
     public bool kJoystikEnabled = true;
     public float kJoystickSpeed = 0.5f;
     public bool kInverse = false;
     public float kMovementSpeed = 10;
  
     Transform ownTransform;
     Transform cameraTransform;
     CharacterController characterController;
     Camera _camera;
  
     int leftFingerId = -1;
     int rightFingerId = -1;
     Vector2 leftFingerStartPoint;
     Vector2 leftFingerCurrentPoint;
     Vector2 rightFingerStartPoint;
     Vector2 rightFingerCurrentPoint;
     Vector2 rightFingerLastPoint;
     bool isRotating;
     bool isMovingToTarget = false;
     Vector3 targetPoint;
     Rect joystickRect;
  
  
  
  
  
     void MoveFromJoystick()
     {
         isMovingToTarget = false;
         Vector2 offset = leftFingerCurrentPoint - leftFingerStartPoint;
         if (offset.magnitude > 10)
             offset = offset.normalized * 10;
  
         characterController.SimpleMove(kJoystickSpeed * ownTransform.TransformDirection(new Vector3(offset.x, 0, offset.y)));
     }
  
  
  
     void MoveToTarget()
     {
         Vector3 difference = targetPoint - ownTransform.position;
  
         characterController.SimpleMove(difference.normalized * kMovementSpeed);
  
         Vector3 horizontalDifference = new Vector3(difference.x, 0, difference.z);
         if (horizontalDifference.magnitude < 0.1f)
             isMovingToTarget = false;    
     }
  
  
  
     void SetTarget(Vector2 screenPos)
     {
         Ray ray = _camera.ScreenPointToRay (new Vector3 (screenPos.x, screenPos.y));
         RaycastHit hit;
         int layerMask = 1 << 8; // Ground
         if (Physics.Raycast(ray, out hit, Mathf.Infinity, layerMask)) 
         {
             targetPoint = hit.point;
             isMovingToTarget = true;
         }
     }
  
  
  
     void OnTouchBegan(int fingerId, Vector2 pos)
     {
         if (leftFingerId == -1 && kJoystikEnabled && joystickRect.Contains(pos)) {
             leftFingerId = fingerId;
             leftFingerStartPoint = leftFingerCurrentPoint = pos;
         } else if (rightFingerId == -1) {
             rightFingerStartPoint = rightFingerCurrentPoint = rightFingerLastPoint = pos;
             rightFingerId = fingerId;
             isRotating = false;
         }
     }
  
  
  
     void OnTouchEnded(int fingerId)
     {
         if (fingerId == leftFingerId)
             leftFingerId = -1;
         else if (fingerId == rightFingerId)
         {
             rightFingerId = -1;
             if (false == isRotating)
                 SetTarget(rightFingerStartPoint);
         }            
     }
  
  
  
     void OnTouchMoved(int fingerId, Vector2 pos)
     {
         if (fingerId == leftFingerId)
             leftFingerCurrentPoint = pos;
         else if (fingerId == rightFingerId)
         {
             rightFingerCurrentPoint = pos;
  
             if ((pos - rightFingerStartPoint).magnitude > 2)
                 isRotating = true;
         }
     }
  
  
  
     void Start ()
     {
         joystickRect = new Rect(Screen.width * 0.02f, Screen.height * 0.02f, Screen.width * 0.2f, Screen.height * 0.2f);
         ownTransform = transform;
         cameraTransform = Camera.mainCamera.transform;
         characterController = GetComponent<CharacterController>();
         _camera = Camera.mainCamera;
     }
  
  
  
     void Update ()
     {
         if (Application.isEditor)
         {
             if (Input.GetMouseButtonDown(0))
                 OnTouchBegan(0, Input.mousePosition);
             else if (Input.GetMouseButtonUp(0))
                 OnTouchEnded(0);
             else if (leftFingerId != -1 || rightFingerId != -1)
                 OnTouchMoved(0, Input.mousePosition);
         }
         else
         {
             int count = Input.touchCount;
  
             for (int i = 0;  i < count;  i++) 
             {    
                 Touch touch = Input.GetTouch (i);
  
                 if (touch.phase == TouchPhase.Began)
                     OnTouchBegan(touch.fingerId, touch.position);
                 else if (touch.phase == TouchPhase.Moved)
                     OnTouchMoved(touch.fingerId, touch.position);
                 else if (touch.phase == TouchPhase.Canceled || touch.phase == TouchPhase.Ended)
                     OnTouchEnded(touch.fingerId);
             }
         }
  
         if (leftFingerId != -1)
             MoveFromJoystick();
         else if (isMovingToTarget)
             MoveToTarget();
  
         if (rightFingerId != -1 && isRotating)
             Rotate();
  
     }
  
  
  
     void Rotate()
     {
         Vector3 lastDirectionInGlobal = _camera.ScreenPointToRay(rightFingerLastPoint).direction;
         Vector3 currentDirectionInGlobal = _camera.ScreenPointToRay(rightFingerCurrentPoint).direction;
  
         Quaternion rotation = new Quaternion();
         rotation.SetFromToRotation(lastDirectionInGlobal, currentDirectionInGlobal);
  
         ownTransform.rotation = ownTransform.rotation * Quaternion.Euler(0, kInverse ? rotation.eulerAngles.y : -rotation.eulerAngles.y, 0);
  
         // and now the rotation in the camera's local space
         rotation.SetFromToRotation(    cameraTransform.InverseTransformDirection(lastDirectionInGlobal),
                                                     cameraTransform.InverseTransformDirection(currentDirectionInGlobal));
         cameraTransform.localRotation = Quaternion.Euler(kInverse ? rotation.eulerAngles.x : -rotation.eulerAngles.x, 0, 0) * cameraTransform.localRotation;
  
         rightFingerLastPoint = rightFingerCurrentPoint;
     }
  
 }