Roberto Maroni, the president of Lombardy and founder of the anti-immigrant Northern League, was quoted by TGCom24 as saying, “We do not want an invasion”.
The Veneto region has also shut the door on migrants, with its president Luca Zaia saying there are are “no places" for them.
Marcello Pitella, the president of Basilicata, on the other hand, said the southern region would host “double the number of migrants” in its territory.
The mayor of Bologna, in Emilia Romagna, has also agreed to find room.
“In my opinion, given the extent of the number of arrivals, we need an effective change of pace in order to give a useful solution to those who arrive in our country, as well as to change the climate of exasperation agitated by the xenophobic right,” Valerio Merola was quoted by TGCom24 as saying.
A surge in attempted illegal crossings from the coast of north Africa saw nearly 8,500 migrants rescued between Friday and Monday, reigniting a debate in Italy over whether or not the country has a duty to house all new arrivals.
One of the vessels capsized off the Libyan coast on Sunday, with up to 400 people thought to have died.
The Interior Ministry on Monday called on Piedmont, Lombardy, the Veneto, Tuscany, Emilia-Romagna and Campania regions to find 700 places each for the latest arrivals.
Puglia in southern Italy was told to find 300 places, while the Lazio and Marche regions were asked for another 250 each, with the remaining 1,500 beds to be divided between other regions.
Members of the opposition have accused premier Matteo Renzi's centre-left government of pandering to those fleeing war zones or poverty, with many saying the policy of rescuing immigrants at sea encourages others to attempt the journey.
"It is an absolute disgrace that the government, instead of repelling the invasion of clandestine immigrants, thinks to appropriate thousands and thousands of beds, giving in to the invasion," said senator Maurizio Gasparri from the centre-right Forza Italia party.
Matteo Salvini, head of the Northern League, which has made the crisis one of its platforms ahead of regional elections in May, called on the party’s “governor mayors, assessors and councillors to say no, with every means, to every new arrival.
"The League is ready to occupy every hotel, hostel, school or barracks intended for the alleged refugees,” he said on Facebook.