Matteo Renzi warned that leaving the EU would be a "very difficult process" - but the problems could be solved only after the UK began the exit procedure.
He said the Brexit vote had been "a bad decision" but had to be respected.
Mr Renzi said he was ready to work with UK PM Theresa May to build the "best alliance" between the UK and the EU.
Mr Renzi said he had been shocked and saddened by the EU referendum result, but repeated Mrs May's vow that "Brexit is Brexit", saying democracy had to be respected.
Asked about whether there could be "flexibility" over EU rules on freedom of movement and access to the single-market, he said "I think this is a very interesting debate, because this debate will be a debate about the concept of rules in the EU."
But he said that debate could only begin once the UK had triggered article 50 - the official procedure for it to start leaving the EU - and he warned: "It will be impossible to give to British people more rights than other people outside the EU."
"The people of the UK decided the way for the future," Mr Renzi said. "Now the situation is that we can - and we have to - build the best alliance between the UK and the EU for the future because we will be the best friends for the next years.
"And at the same time I think this decision could push European leaders to invest in a new way for Europe."
Mr Renzi said Brexit discussions would be handled by the European Commission - not individual leaders or countries.
However, he added that he was ready to work with Mrs May "to support this very difficult process".
He said questions over the UK's departure from the EU need to be solved "as soon as possible".
Mr Renzi also blamed Brexit on David Cameron, saying the former UK PM had tried to solve internal problems within the Conservatives by called the EU referendum.
The Italian prime minister, who has called his own referendum in Italy on whether to restructure the country's parliamentary system, said: "The problem was one problem.
"When David Cameron decided to use a referendum to solve some internal problems of the Conservative Party, this was the problem. We cannot use foreign affairs to solve internal problems."