"It is not necessary that they agree on what the CPI-M stands for," Karat said in the interview done in New Delhi.
"But some concrete common political and economic programme has to be there and not just electoral adjustment to win a few more seats. These parties and forces have to be part of the mass struggle to bring an alternative programme.
"It would take time to build up such an alternative front. But conditions are favourable and we shall work towards that front with a common policy programme. It may not happen in the very near future."
He said a Third Front alternative to the Congress and the BJP would "envisage some commonality of views among the parties that come together".
In his interview, Karat made it clear that although the CPI-M and its Left allies were supporting the Congress-led United Progressive Alliance (UPA), they would never support the government's free-market economic policies.
He said the reason the CPI-M was more opposed to the BJP was because "communal forces and those advancing the cause of neo-liberal pro-multinational agenda are in general the supporters of imperialism.
"We have helped the defeat of the communal forces. But the task is not over.
"Communalism has not been totally vanquished. Our task now is while fighting the communal fascist forces, struggle to defeat the harmful economic policies and fight for alternative policies.
"Our experience is that all ruling class parties do not basically differ on economic policies. So when we fight against the neo-liberal economic agenda, it is a general direction and should not be seen in reference to Congress alone."
Karat said the Left was not seeking, for now, to usher in socialism in India.
"The present role of the Left in a parliamentary democracy is a progressive role. It is not the end in itself. We struggle to bring some respite to people."
Karat also warned his party colleagues from becoming lethargic in view of the crucial role being played by the Left vis-à-vis the present government.
"My experience of working in Delhi and other northern India states tells me that there are no short cuts," he said.
"We have to guard against our state leaders and cadres becoming lethargic... We have to see that our independent activity does not suffer... Another is to see we work out strategies to turn the present caste struggles into class struggles.
"In India, the distinction between the class and the caste gets blurred for the simple reason that those on the lower ladder of the caste are often the most poor and part of the proletariat.
"We have to devise strategies without losing sight of the class struggle."