The fight against the Covid-19 pandemic in India appears to be a "demonstration of one-upmanship" between states and the Centre, Moily said.
It is shocking to see that the total focus in this fight has been lost, he added.
There are fundamental questions on which there has been no assurance through any of the actions of states or the Centre, Moily said.
He called for universal testing to fight the pandemic.
Moily also posed questions for Prime Minister Narendra Modi like whether the capacity of testing has been properly assessed state-wise or any action has been taken to enhance the testing facilities.
He also asked whether any concrete measures have been worked out to meet the serious question of hunger arising out of the present crisis and whether appropriate livelihood programmes have been worked out for migrant and unorganised labourers.
Moily said the government should make clear what measures have been planned for mobilising scientists and researchers to invent vaccines for the infection.
He also asked whether post-COVID-19 rehabilitation and restoration measures have been worked out to resolve the problem of employment, hunger or economic revival.
Moily urged Prime Minister Modi to answer the key questions in the battle against COVID-19.
The former Union minister is part of the Congress task force set up last month to intensify efforts to deal with the COVID-19 situation in states in which it is the ruling party.
Besides Moily, the task force also includes P Chidambaram, Jairam Ramesh and Tamradhwaj Sahu.