In a communication to state governments and union territories, the home ministry said there have been several incidents of violence against Covid-19 frontline healthcare professionals, complete violation of social distancing norms and movement of vehicles in urban areas. These should be stopped, it said.
The death toll due to Covid-19 rose to 543 and the number of cases climbed to 17,265 in the country on Monday, according to the Union health ministry.
The situation is "especially serious" in Indore in Madhya Pradesh, Mumbai and Pune in Maharashtra, Jaipur in Rajasthan, and Kolkata, Howrah, East Medinipur, North 24 Parganas, Darjeeling, Kalimpong and Jalpaiguri in West Bengal, the ministry said.
"Violation of lockdown measures reported, posing a serious health hazard to public and risk for spread of Covid-19," it said.
The central government has constituted six Inter-Ministerial Central Teams (IMCTs) to make on-spot assessment of the Covid-19 situation in these places and issue necessary directions to the four states -- Madhya Pradesh, Maharashtra, Rajasthan and West Bengal -- for redressal.
The teams will submit their report to the central government in the larger interest of the general public, the ministry said.
"The IMCTs will focus on compliance and implementation of the lockdown measures as per guidelines, supply of essential commodities, social distancing, preparedness of health infrastructure, safety of health professionals and conditions of relief camps for labourers and poor people," a home ministry spokesperson said.
The lockdown was first announced by Prime Minister Narendra Modi on March 24 in a bid to combat the coronavirus pandemic. It was further extended till May 3.
 "A man wearing protective suit checks the temperature of people standing in a queue")