There is really no need of importing a public key. It is public after all, it is designed for everyone to eventually know it.
You need a private key to use your bitcoins, that is what you should be importing in Bitcoin Core.
I believe they start with xpriv...
I believe it is BIP38 encrypted and you should find an opens source program to decrypt it. You can use
https://www.bitaddress.org , it is also available on GitHub and you should download the code and run it offline.
Can you post a step by step guide? I would like to access my blockchain.info funds from Bitcoin Core. I believe I can only to this if I import somehow the private key from blockchain.info into Bitcoin Core. But I can't seem to find from where do I get the private key from blockchain.info. Please advise.
I don't use online wallets, they are not secure, but I found this topic for you
https://bitcointalk.org/index.php?topic=2063572.0 .
Just follow the first part on exporting your private key from the blockchain.info
This should give you the xpriv key. Then go to
https://github.com/pointbiz/bitaddress.org/releases download the latest version's source code in zip format.
Unplug your Internet cable.
Unzip it and I guess you open a file bitaddress.org.html in your browser.
Then go to "Wallet Details" tab, put your private key in and I guess it should tell you your private key at "Private Key WIF".
Then open Bitcoin Core, go to Help->Debug Window and click the "Console" tab. There type in "importprivkey <your private key>".
You should encrypt your wallet as well before hand if you didn't already by going to Settings->Encrypt wallet...
