Can 1000w inverter with a peak power of 2000w be able to power a 160L refrigerator
Depending on the motor type used in the fridge, they can have a very high starting VA.
I saw a design several decades ago which was a battery power supply for a fridge. It used a 2-stage design. The first was a low power boost converter (a few hundred watts) to a 300 V DC bus, the second was a high current H-bridge which could handle the 1 kW VAr needed for the motor startup through its DC bus capacitors.
You maybe have enough power in reserve to do it in one device. Try it and see.