I am wondering if possible to find an op-amp with high output current up to 600 mA. We have +/- 5 V available for biasing of the op-amp but the load requirement is 600 mA which I am not sure can be supported by op-amp or not. Any suggestion ?
First you need to define the application requirements.
(you said that you have +/-5V available. I guess this means power supply voltage. But what about power supply current, load voltage, input signal voltage, frequencies...)
And as so often .... is it asking too much for a simple sketch? It really could speed up to find a solution and prevent from misunderstandings.
Did you do a search (selection tool) at your electronics distributor ... or at an OPAMP manfacturer?
That´s what I´d do.
There are several options, you should talk about bandwidth, output swing. Audio power amps may be a solution, DSL drivers if high bandwidth is required.