Tribals reached the minister's residence in Wada taluka in the early hours and started shouting slogans against Sawra, who is also the guardian minister of the district.
The protesters, under the banner of Shramjivi Sanghatana, alleged that the minister is not paying attention to the malnourished children and sought an explanation from him.
Sawra, who had earlier reportedly said that there were no malnourished children in Palghar, admitted that there were such children who needed attention and medical assistance.
The agitators lamented the central government's decision to discontinue the Village Child Development Centers (VCDC) programme. The minister assured them of starting a new scheme on the lines of the VCDC in the next eight days, which would be funded by the Tribal Development department.
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Sawra also said that he would take up the problem of malnutrition with the state Chief Minister Devendra Fadnavis.
A meeting of the secretaries from the departments of the Health, Tribal Development and Women and Child Welfare, and representatives of the Shramjivi Sanghatana would be held soon to resolve the issue, the minister said.
"If the minister fails to keep his promises and does not follow the timeline, we would stage an agitation at Varsha, the official residence of the state Chief Minister," Vivek Pandit told reporters.
According to an official statement, the number of malnourished children, falling under SAM (severe acute malnutrition) and MAM (moderate acute malnutrition), in Palghar district is over 5,500.