The eurozone's third largest economy is heavily dependent on Russian gas, but has been seeking new sources since Moscow's invasion of Ukraine, including with a deal to boost supply from Algeria.
Addressing the Senate, Draghi said his government was also seeking to boost its production of renewable energy, including by "destroying bureaucratic barriers" to investment, saying it was the "only way" to free Italy from having to import fossil fuels.
"Government estimates indicate that we can make ourselves independent from Russian gas in the second half of 2024," he told lawmakers, while adding that the "first effects" of this plan would be felt by the end of this year.
In April, Italy's Ecological Transition Minister Roberto Cingolani estimated the country would no longer need Russian gas within 18 months, following an earlier prediction that it could take up to three years.
In 2021, 40 percent of the natural gas that Italy imported came from Russia.
Draghi repeated his strong support for EU sanctions on Moscow, including a proposed ban on imports of Russian oil, although this is currently being blocked by Hungary.
"We must continue to keep up the pressure on Russia through sanctions, because we must bring Moscow to the negotiating table," he said.