Whether you should push yourself more depends on how old you are, how fit you are, how you feel during the interval/blast stage.
When I am done with a hard running interval, at this current stage of my fitness and aged 44, my pulse rate can be between 28 bpm (168) at the lowest end of the range and 30 bpm (180) at the high end. This feels comfortable for me and I know I am working hard. I take the full minute or two minutes to recover, length of recovery stage depends upon how hard I pushed the interval and whether I preceded my interval workout with a 20-40 min steady state run or not, and gauge my need for rest based on how I feel.
Sounds like you could experiment with reducing the resting stage to 1 minute. However, bare in mind that the resting stage is supposed to be longer than the interval/blast stage. Adequate resting stage enables you to push harder in the blast stage. Don't short change yourself.
Clare