Current ratings are a capacity rating. Electronics only draw the amount of current they need. So if you have a 1000mA source and your electronics (such as the Arduino) only draws 50mA, it will still only draw 50mA.
The challenge here is that when powered through the USB port of the Arduino, there is an on board fuse that limits current to 500mA. So even if your source is 1000mA capable, the Arduino will not allow drawing full capacity.
The alternative is to hook the battery directly to the 5V node, which bypasses the on-board fuse.
Thank you for the answer. Now I am safe to use it