An editorial in the CPI-M journal "People's Democracy" said it would be "a tough proposition" for the BJP to do well in Assam and show that it was a growing force in West Bengal, Tamil Nadu, Kerala and Puducherry.
Staggered elections in the five states will begin on April 4 and end on May 16. The vote count will take place on May 19.
"These elections are important not only because it will determine who will form the state governments there, but it will also have a bearing on the future course of national politics," it said.
"The BJP alliance, which has a comfortable majority in the Lok Sabha, has not been able to maintain the momentum.
"After the initial victories in Maharashtra, Jharkhand and Haryana assembly elections, the BJP began to lose ground," it said, referring to the defeats in Delhi and Bihar last year.
"This time around, the BJP is not a major force in these states, except for Assam.
"But apart from doing well in Assam, it has to show that it is a growing force in the other states. This is going to be a tough proposition."
For the Left, including the Communist Party of India-Marxist, these elections were crucial because of West Bengal and Kerala, the editorial said.
It said the Left was "poised to deal a terminal blow" to the Congress-led government in Kerala "and to set the state on a fresh path".
In West Bengal, it said, the Left was "fighting an arduous struggle in defence of democracy and against hoodlum terror".