Time magazine's cover labelling Manmohan Singh as "the underachiever" prompted heated debate in India.
Using Time's words on Mr Singh, Outlook reads: "America needed a reboot".
Outlook's editor denied the cover was a "tit-for-tat" response to Time or an expression of support for Mr Singh.
But the words on the cover of the magazine reads: "He promised hope and change. Four years on, President Barack Obama's sheen is gone. Can his lofty rhetoric carry him home again?"
Time on its cover had asked a similar question: "India needs a reboot. Is Prime Minister Manmohan Singh up to the job?"
India's government has recently come under heavy criticism for what many are calling "policy paralysis".
'Focus on Obama'
Outlook's editor told the BBC that they had been "planning an Obama cover for a long time" and that it was "not tit-for-tat" journalism.
"Our focus is not Time magazine. Our focus is Mr Obama.
"We are trying to do the American election in a slightly different way. We are trying to take a long, hard look at Obama and his performance in the last four years," Krishna Prasad says.
Mr Prasad said their story was about "Mr Obama's performance vis-a-vis India, the world and within America".
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