The former Chief Minister, now in Delhi to take part in a Central committee meeting, has sought a course correction in Vijayan's functioning and urged the leadership to intervene "appropriately".
The letter comes as the Vijayan government is set to complete one year in office but has seen the resignation of two cabinet ministers.
While Industries Minister E.P. Jayarajan quit over charges of nepotism, Transport Minister A.K. Saseendran resigned after an audio clip emerged in which he is heard having lewd talk with a woman.
Achuthanandan and Vijayan have been at loggerhead for a long time. When Achuthanandan was the Chief Minister, Vijayan had complaints against his government.
Meanwhile, the Central Committee meeting in Delhi on Wednesday decided to warn Jayarajan and Lok Sabha MP P.K. Sreemathi over nepotism charges.
Jayarajan quit after it surfaced that he had appointed the son of Sreemathi to a top post in a state government undertaking, overlooking qualified candidates who had applied for the post.
(This story has not been edited by Business Standard staff and is auto-generated from a syndicated feed.)