Generate a public key from private key

openssl genrsa -out mykey.pem 1024

will actually produce a public – private key pair. The pair is stored in the generated mykey.pem file.

openssl rsa -in mykey.pem -pubout > mykey.pub

will extract the public key and print that out. Here is a link to a page that describes this better.

openssl rsa -in key.pem -pubout -out pubkey.pem

To get a usable public key for SSH purposes, use ssh-keygen:

ssh-keygen -y -f key.pem > key.pub

This public key format is compatible with OpenSSH. Append the public key to remote:~/.ssh/authorized_keys and you’ll be good to go

ssh-keygen -y [-f input_keyfile]
-y This option will read a private OpenSSH format file and print an OpenSSH public key to stdout.

docs from SSH-KEYGEN(1)