unable to update – multiple error messages

Running WP 4.2.2 on a host’s server. Been using WP for several versions, and only started having update problems recently.

First issue:
On the Dashboard->updates page, I have the following text:

Warning: An unexpected error occurred. Something may be wrong with www.remarpro.com or this server’s configuration. If you continue to have problems, please try the support forums. (WordPress could not establish a secure connection to www.remarpro.com. Please contact your server administrator.) in /Volumes/Extra/www/familymedia/wp-admin/includes/plugin-install.php on line 83

This appears three times above the box showing the three plug-ins to be updated. I have had this message for a while. It didn’t seem to affect anything and I could not find a solution, so I let it slide.

Now, when attempting to update ANY plug-in, I get the following error message:

An error occurred while updating Contact Form 7: Download failed. SSL certificate problem, verify that the CA cert is OK. Details: error:14090086:SSL routines:SSL3_GET_SERVER_CERTIFICATE:certificate verify failed

Attempt to update themes results in same message:

An error occurred while updating Twenty Fifteen: Download failed. SSL certificate problem, verify that the CA cert is OK. Details: error:14090086:SSL routines:SSL3_GET_SERVER_CERTIFICATE:certificate verify failed

Finally, attempting to update the WP install to the current 4.3.1 version results in:

Download failed.: SSL certificate problem, verify that the CA cert is OK. Details: error:14090086:SSL routines:SSL3_GET_SERVER_CERTIFICATE:certificate verify failed

I have searched the forums and found no solution. On suggestion involved replacing the “ca-bundle.crt” file. That did not work for me. Another solution suggested replacing the “update.php” file. That did not work either.

I contacted my host and he response was “Everything should be fine on the server side. You’d need to contact wordpress’ support accordingly. “

Any help would be very much appreciated.