The next cumulative update is available.
Be aware that all Updates for SharePoint 2013 require March 2013 PU for SharePoint 2013 to be installed first.
SharePoint Foundation 2013
2817346 The full server package for SharePoint Foundation 2013
SharePoint Server 2013
Unfortunately we cannot provide the hotfix packages yet, these are delayed.
I will update my blog with a Part 2 post when these are available. You might also check the blog post from my colleague: http://blogs.technet.com/b/stefan_gossner/archive/2013/06/12/june-2013-cu-for-sharepoint-2013-is-delayed.aspx
Office Web Application Server 2013
2817350 Microsoft Office Web Apps Server 2013 hotfix package
SharePoint Designer 2013
2768343 SharePoint Designer 2013 hotfix package
Important for all Server Applications listed above:
After applying the preceding updates, run the SharePoint Products and Technologies Configuration Wizard or “psconfig –cmd upgrade –inplace b2b -wait” in command line. This needs to be done on all servers in the farm with SharePoint installed. You can run psconfig in parallel on all SharePoint machines.
You might have you own strategy to run psconfig because it depends on the farm structure and what makes sense to reduce the downtime.