Can I use 6V 1300mAH NimH charger (http://www.robosoftsystems.co.in/roboshop/index.php/electronics-batteries/batteries-chargers/charger-for-6v-1300ma-battery.html) to charge 6V 1600mAH NimH battery pack(http://www.lynxmotion.com/p-331-60-volt-ni-mh-1600mah-battery-pack.aspx)?

It seems you can give a try. don't you have any other charger?

Nope. I had http://www.lynxmotion.com/p-602-60-12vdc-ni-cd-ni-mh-universal-smart-charger.aspx. But it's not working. I cudn't fix it, the SMD  on the board is completely burnt. I need an alternative. Turnigy NiMH charger is available in India but very expensive.

In my opinion you should buy a proper charger that charges li poly, NiMH etc.

That charger charges NiMH battery packs. Same voltage 6V but the mAh rating is 1300mAh instead of 1600mAh..

The current rating differs. If your charger is working properly than you can surely charge your battery with it.