Conte, yang jarang muncul di hadapan umum dan dua kali dirawat di rumah sakit di Swiss tahun lalu, sejauh ini telah menampik tuntutan tersebut dan menyeru militer agar mendukung pemerintahnya.
Conte, who is rarely seen in public and was twice hospitalised in Switzerland last year, has so far dismissed the demands and called on the military to back his government.