He also pledged to meet the widower of an Italian woman allegedly beaten to death by a Romanian immigrant last year "and promise him that what happened to his wife would never happen again".
Alemanno is a key ally of Silvio Berlusconi, who was elected Italy's prime minister earlier this month.
He rose through the political ranks from the youth branch of a neo-fascist party who blamed the previous centre-left administrations for allegedly tolerating crime by immigrants.
"This tolerance has generated in Europe and the whole of the mediterranean the idea that you can come to Rome and do what you want," he said in his final television debate with his opponent, Francesco Rutelli, the former mayor of Rome, last week.
"This has attracted flows of gypsies and migrants, who came to Rome precisely because they knew they would have no rules, no limits."
The rape of a woman, allegedly by an immigrant, 10 days before the election was seen as a factor in the vote.
It recalled the fatal beating of the Italian woman last autumn.
Soon-Sub Chun, a freelance journalist from North Korea who has lived in Rome for 10 years, said doors should not be closed to immigrants.
"For us, it is a very delicate problem. Those who are legal can live in peace but those without papers are always in fear," he said.
"There should be a way to welcome and help them, too."
Deepa Tisera, 40, a hotel worker from Sri Lanka who moved to Rome nine years ago, said: "I've always had proper documents, so I am not worried.
"We need to wait and see what kind of laws he is going to pass."
Italian newspapers recently carried a report from the interior ministry stating that some 35 per cent of the crimes in Italy between January and August 2007 were committed by immigrants, mostly illegal.
Meanwhile, a study released on Tuesday indicated that most Italians have negative views about immigrants from Muslim countries.
According to the study carried out by the Makno research organisation, and commissioned by Italy's interior ministry, 55 per cent said immigration from Muslim countries was more problematic than that from Christian or other countries.
About 40 per cent said Muslims should be allowed to practise their religion and build mosques unconditionally.
Almost 10 per cent were firmly against allowing Muslim religious practices or mosques to be built.
Nearly 40 per cent of Muslim immigrants said they found it difficult to honour their religious traditions in Italy while 30 per cent feared they would lose their culture.