A commentary by CPI-M general secretary Prakash Karat said while the AAP seeks to tackle some critical problems faced by the people, it was "silent on the nature of the economic policies which have produced these problems".
The commentary, in the CPI-M journal "People's Democracy", said rising electricity rates were due to the privatisation of power distribution in Delhi. "The high level institutionalized corruption is an outcome of the neo-liberal regime. So is the contractised work pattern."
"But the AAP is yet to spell out its comprehensive policy platform. Do they advocate any alternative policies to neo-liberalism?
"There seems to be a tendency to gloss over these matters, perhaps due to the contradictions that exist in the social base which has rallied around in the party."
The CPI-M admitted that the rapid rise of the Aam Aadmi Party "has been generally welcomed by the democratic and secular circles".
"The AAP's rise has been unique in that it could build a network and gather support from the middle classes and extend its influence amongst the poorer sections in the setting of a metropolitan city."
It said the AAP's success "is a positive development".
"The involvement of a normally apolitical middle class and attracting the youth to political activism with idealism is a singular achievement...
"The AAP has effectively checked the BJP's advance and exposed their corruption and policies which are similar to those of the Congress. Narendra Modi's appeal to the middle class and the youth was blunted by the AAP campaign in Delhi."
AAP's success "is a positive development: CPI-M general secretary Prakash Karat
But it said the AAP's stand on communalism and the Hindutva agenda was absent. "Can the AAP ever hope to present itself as an alternative without taking a clear-cut stand against communalism?"
Karat said now that the AAP was planning to fight elections in other states, it was all the more important that it should spell out its basic programmes and policies.
"Only then, will it be possible for the people to determine the nature of the party and the direction it will take."
The CPI-M said the AAP's plank of fighting the "political establishment" tarred all political parties with the same brush, the Left included.
The commentary said that the virtues that AAP claims for itself - a clean image, incorruptibility, denial of perks and privileges of power and funding based on people's contributions - "are all part of the style and practice of the communists from the outset".
It said the CPI-M had always relied on mass contributions of small amounts and the levy paid by party members as the main source of its funding.
"The citizens of Delhi have appreciated the refusal of Kejriwal and his other ministers not to seek large official accommodations and to stick to their modest housing.
"This is the tradition set by communist leaders in public office... The Left-led governments have always adhered to these values."
Karat accused the Congress and the BJP of heaping "burdens on the people" and favouring "the interests of the international finance capital and Indian big business".
"The neo-liberal regime they uphold is the fountainhead of high level corruption."
It said there were very few parties, apart from the Left, with policies different from those of the Congress and BJP.
"The AAP is at an important crossroads after the Delhi elections. Will it be able to spell out an alternative policy direction and build a party which will represent the interests of the aam aadmi and the working people of the country?
"On this will depend the future trajectory of this novel political formation."