To add to the government's woes, senior CPI-M leader, V S Achuthanandan also hit out, saying exemplary action should be taken against the wrongdoer.
When asked about the ongoing row over the appointments, Vijayan told reporters in Kozhikode: "The issues which have cropped up now, the government viewed them seriously. We will decide together and take an appropriate decision."
"LDF is not UDF, CPI(M) is not Congress," he added.
Asked whether the present controversy had tarnished the image of the LDF government, Achuthanandan said: "There is no doubt (about it)."
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"I think the government will conduct a serious inquiry into the issue and take exemplary action against the wrongdoer," he told reporters in Thiruvanathapuram.
When asked about the statement of Achuthanandan, who is also Chairman of Administrative Reforms Commission, Vijayan did not react.
Vijayan, who was party secretary then, said ministers can appoint three persons in their personal staff-- a cook, driver and a person to answer the telephone.
The party was not aware of the appointment of Sreemathi's daughter-in-law and no prior permission need be taken from the party for it as the minister concerned can decide, he said.
However, when she was promoted, it came to the party's notice and it was felt that was not appropriate and the appointment was struck down, he said.
daughter-in-law's appointment was "with the party's knowledge."
When the controversy broke out, she resigned as per the party's directive. "But, she is not receiving any (government) pension as alleged by Congress and BJP leaders. She has not even applied for it," the former minister clarified.
However, she later withdrew the post following criticism from various quarters.
Meanwhile, Opposition leader Ramesh Chennithala today dragged Chief Minister Pinarayi Vijayan into the row and said Vijayan's stand he was "unaware" about the controversial appointments was "not correct."
He also wanted the government to quash appointments of leaders' relatives in PSUs.
"Accused should be punished under anti-corruption law. Vigilance and Anti-Corruption Bureau should take action in this," he said adding that Jayarajan had no moral right to continue in the position.
BJP state secretary M T Ramesh also demanded Jayarajan's resignation.
The minister should be expelled from the government if he was not ready to go out himself, Ramesh told a press meet in Thiruvanathapuram.
He also said the party would approach court, soon after the pooja holidays, seeking action against Jayarajan.