Unable to install OS X, cmd+R opening internet recovery instead of usual recovery

I'm trying to clean install OS X El Capitan on a MacBook Pro (early 2015).

After erasing my disk I started the installation of OS X. After accepting the license agreement I was asked to choose a target drive. I hesitated a little bit and wanted to cross-check if I have created the partitions correctly so I canceled the installation. There were no options to go back to Disk Utility so I restarted my machine.

Now when I press cmd+R, it always leads me to internet recovery. The only thing I saw was a spinning globe and I was asked to choose a Wi-Fi connection. I connected to my Wi-Fi network and still only saw a spinning globe. After waiting for a long time it has shown the error apple.com/support 2002f

How can I access the normal recovery mode and install OS X?

Your model Mac was shipped with Yosemite (OS X 10.10) installed. The tags you placed on the question suggest you have upgraded to El Capitan (OS X 10.11). There is the possibility you could have erased the Recovery partition by using the Disk Utility if you had Yosemite installed. Evidently, this would be much harder (or perhaps impossible) to do if El Capitan was installed. Also, I do not know if you were using Core Storage and if so, how this would effect the ability to erase the Recovery partition.

Evidentially, you can now only boot using OS X Internet Recovery. You can use Internet Recovery to install the version of OS X that came with your machine. From this, you can go to the App Store and download and install newer versions of OS X.

An alternative would be to use another Mac to download OS X. You can then transfer the download to a USB drive. You then use the USB drive to install OS X on your Mac. The instructions are given the Apple web site: Create a bootable installer for OS X.

I have a workaround for this problem. It seems somehow my system hates my Wi-Fi connection (may be due to some encryptions related to Wi-Fi). When I went to my friend's place and connected to Wi-Fi, I was able to proceed with Internet Recovery. After waiting 5 minutes, I landed on a page similar to normal recovery mode and then I was able to install OS X normally (Yosemite was installed in this case).

If this doesn't work, I would have create a bootable installer for OS X as suggested by David's and bmike's answer