Can EC2 instances in different regions communicate

I have two EC2 instances from an Ubuntu image, they are located in different regions. I just want to ask, whether they can communicate over the private IP addresses?

I have opened the required ports with a security group. I use netcat to test the communication, but it only works, when I use the public IP addresses.

It is not possible to communicate between Amazon EC2 regions via the private IP addresses (except if you setup a VPN and respective routing for this, see section VPN Solution below), traffic between regions is in fact passing the public internet and is not distinguishable from any other internet traffic, see e.g. the following FAQs from the Region and Availability Zone FAQ:

Can instances use group-based firewall rules across Regions? - No. Group-based firewall rules only work within a Region. If you need instances to communicate with each other across Regions, you should use CIDR based firewall rules. [...]
What is the cost for data transfer between Regions? - Data transferred from one Region to another is charged at both sides at the Internet data transfer rate.

This applies to an Amazon VPC as well, see e.g. the FAQ Can Amazon EC2 instances within a VPC in one region communicate with Amazon EC2 instances within a VPC in another region?:

Yes, as long as all communication takes place over the Internet Gateway of each VPC and uses the Elastic IP addresses assigned to the instances in each VPC. Please note: security groups cannot span regions. All traffic filtering between instances in one VPC and instances in another VPC must use the Elastic IP addresses as the specified source or destination address. [emphasis mine]

VPN Solution

AWS has meanwhile released two walkthroughs describing a solution for Connecting Multiple VPCs with EC2 Instances based on either IPsec or OpenVPN:

Connecting Multiple VPCs with EC2 Instances (IPSec)
- please note that this tutorial facilitates Openswan, but you can achieve the same with strongSwan (or even the Linux IPsec stack built in as of kernel 2.6+, see e.g. IPsec L2TP VPN server)
Connecting Multiple VPCs with EC2 Instances (SSL)