Is a 4x4 essential in Iceland at end of August?

We are making a 4 day trip to Iceland from 24-28 August 2013.
We want to rent a car. We heard that the F-roads (for which you would need a 4x4) are normally closed in August.
Questions:
- Are the f-roads normally closed at end of August?
- If they are closed, is it still worth getting a 4x4? Do you need it on the normal roads?
We don't mind driving quite a bit and would like to get to the eastern glacial if possible.
Best Answer
Just as an update...
We did eventually hire a Chevrolet Captiva 4x4, which was a great car to drive around.
We didn't actually make it onto the F roads, but ended up having to drive on gravel tracks, which were probably pretty much the same.
The only problem we had, was that this car which is a 4x4, aka all-wheel-drive, got stuck drive through some mud.
I then remembered that you really need Differential lock, to be able to drive out of mud, as both front and back wheels on one side were stuck.
If only front OR back wheels had been stuck, it wouldn't have been a problem, but it was both right hand side wheels were stuck and therefore the left hand side wheels just kept spinning.
Just a word of caution. We didn't drive through a river, it was a larger puddle...quite annoying. But a brilliant local turned up and pulled us out with a massive rope!
Enjoy!
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Do I need a 4x4 for Iceland?
A 4WD is required by law to go on Iceland's F-Roads (mountain roads). They're not necessarily in the mountains either. In addition to places like the Highlands, Landmanalaugar, etc. you'll also find F-Roads in places like the parts of the Diamond Circle or the Westfjords.Do you need AWD in Iceland summer?
2WD in Iceland General rule of thumb is that if you're coming during the summer months a two wheel drive will be just fine. That's the general rule of thumb.Do you need a 4x4 for Ring Road Iceland?
If you plan on exploring the Highlands, you absolutely need a 4-wheel drive in Iceland. If you're just going to make your way around the Ring Road, you don't. And if you're coming between the winter months of November to March, I would recommend a 4WD vehicle. Hope this cleared some things up.Do you need an SUV to drive around Iceland?
It's forbidden to drive Iceland's F-Roads without a 4X4 vehicle due to the rough conditions. Traveling in pairs with a second vehicle is highly recommended, in case one of you breaks down. F-Roads are only open during the summer months, generally June \u2013 September (or first snow).Road Signs in Iceland - All You Need To Know
Sources: Stack Exchange - This article follows the attribution requirements of Stack Exchange and is licensed under CC BY-SA 3.0.
Images: Mikhail Nilov, Stijn Dijkstra, Gylfi Gylfason, Kamil