Air. Lots of air. Hang it where air can get at both sides if you can, or prop it up so that air can get underneath. There's no way to know if it'll stain because of the unknowns of what was in the water. Even if there isn't soap, there could be any number of invisible elements and chemicals it could have picked up along the way. If it's manageable, you could try rinsing the whole run well. That way there's an equal amount of wetting, and maybe rinse out whatever strays might color it, but it's not sure, and that much water could weaken the fibers. It's something you'll have to judge. If you're going to hang it, it'll help to support the bottom, and to put the least amount of weight as possible on the wet area. For a hall rug, that probably means hanging it sideways.

If you have a gun style blow dryer, you can try that, working from both sides, but not so that any of the heat reaches the grass. The air is good, and you can warm it so that it's a little warmer than room temp, but actual heat can also weaken the fibers. Be patient.

If there's a cloth backing, get that as dry as you can as fast as you can, and keep going back to it. It makes airing even more important. The last thing you want is to get mildew. Even when the surfaces seem dry, there will be damp between the grass and the backing, so it's really important to keep airing it, and blowing on it off and on, until it's dry all the way through.

If all of the above sounds like more than you can handle, and if there isn't a cloth backing, you can try just putting a pile of towels under the wet area and changing them out as they get wet. And you can try the non-heating dryer from above.

Volume of air circulating is more important than temperature in a case like this. Get box fan running to move drier air from other rooms into this room also. The more air you can get moving across the surfaces (front and back) the faster it will dry.
Best of luck,
Shaughnn

From what I just read on the care of these rugs, I think I would blot as much as possible and then use a hair dryer or fan. How large is the rug?

Oh! Fan! Great suggestion. If you have several, use them all.

Hundifier. Wait, maybe I mean dehumidifier?
The one that gets the moisture out and of course the
brilliant idea of the box fan.
It will get better.
I think... not sure but Sea grass is one of those beautiful
fibers that can handle water.
Sending Seagrass get well wishes your way.
~boxerpups

Sisal should not be near water. (I hope yours is not sisal)
http://www.theflooringlady.com/sisal_rugs_000736.html

Here is a link that might be useful: Pure Style (She talks about sea grass rug care)

Thanks everyone! I am now having computer issues too! Couldn't get online to see your responses until now when I remembered I had an iPhone. Doh! Fans are a great idea. Fortunately the newly painted ceiling doesn't seem to gave a water mark. Carpet is still wet, but it is seagrass not sisal. It was in water once, so hopefully that
means it can be in water again. I'm off to remove towels and start fans. Thank you all so much! I new gw would have great ideas! This forum is the best!!!

Dotcomgone - I think you'll be fine following the above suggestions to make sure any cloth backing gets dry and to air it out. The fan suggestion is very good too.

I have wall to wall seagrass on my entire 2nd floor and several area rugs on first floor. Lots of kids, pets, & spills. Be glad it was water & not red wine (from experience)! All the soaking water spills we have had have dried up with time leaving no evidence - even the spills on the wall to wall. Let us know how it turns out. Good luck - I bet it'll be just fine!

Dotcomgone, please let us know how this turns out. Good luck!

Thanks again everyone for your responses. I truly appreciate since it wasn't even a kitchen emergency. The fans really helped dry things up yesterday and I'm pleased to say it does not appear that there is a watermark on the carpet. I think it weathered 'the storm'. Phew! The seagrass is backed in rubber, but there was so much water it was soaked through to the wood floors. We had just gotten the seagrass a few weeks ago and I can't imagine a big stain already. Believe it or not same ds tried to make his own breakfast today and dropped the syrup which exploded all over the wool runner in the kitchen. YES REALLY. What a sticky
mess. The little monkey...