AWS: docker container cannot connect to external website on SSL

On my ec2 instance, there is a container hosting a website (e.g. Wordpress). This containers binds container ports 80 and 443 to ports 8080 ad 8081 of the host (both are enabled for inbound traffic in the security group).

The problem is that the website inside the container needs to connect to external websites on SSL, but it fails in doing so.

It looks like a problem of the security group/firewall...but I coudn't detect the specific cause yet, as the security group is now it should work.

If I enter the container, ping of the external website (e.g. wordpress.org) works.

I don't know if it is related, but recently the EC2 instance had problem validating ssl certificates, even the python pip tool wasn't able to validate SSL certificate inside the container.

Any help?