Mr Putin said Russian people knew how New Yorkers felt
Amid tight security, including Russian officials holding automatic rifles, Mr Putin spent several minutes touring the site, where the remains of thousands are still buried.
"He was, like many others, shocked at the extent of the devastation," said Mr Giuliani.
"(He was) very upset about it and supportive of the United States and what we need to do to defend ourselves against terrorism," he added.
Suffering
Mr Putin shook hands with several New York firefighters and signed a wall attached to the platform as a mark of solidarity with the city.
He later went on to the United Nations headquarters to meet UN Secretary-General Kofi Annan.
Mr Putin also took part in an unprecedented live radio programme, answering questions from Americans on topics including Afghanistan, Nato enlargement, his former job as a KGB officer and the conflict in Chechnya.
He spoke of how the Russian people felt the suffering of New Yorkers more than most, as they, too, had suffered from terrorist actions.
He firmly ruled out any role for outside mediators in resolving the conflict in breakaway Chechnya.
No missile agreement
Earlier in Mr Putin's trip it emerged that Russia and the United States had failed to reach agreement on US plans for a missile defence shield, despite three days of talks between the Russian leader and American President George W Bush.
The two men - who met at Mr Bush's ranch near Crawford, Texas - praised each other warmly at a joint press conference on Thursday.
But Mr Bush said they had a "difference of opinion" over missile defence.
Russia strongly opposes Washington's plans to abrogate the 1972 Anti-Ballistic Missile treaty, which bans systems like the one Mr Bush wants.
Mr Bush and Mr Putin also spoke to students at a school in Crawford after their meeting ended.
Mr Bush called the Russian leader a "man who will make a huge difference".
Mr Putin said the US president was "one who does what he says".
Both drew laughter with light-hearted comments about the heat in Texas and the cold in Russia.
But they were unable to paper over the significant differences between their positions with jokes or positive spin.
"We differ in the ways and means we perceive that are suitable for reaching the same objective", Mr Putin said.
Arms reduction
Nonetheless the two leaders did successfully agree to drastically reduce their respective country's nuclear stockpiles.
Mr Putin offered to reduce Russia's long-range weapons by about one-third.
White House officials had earlier warned the media not to expect an accord on missile defence.
"This is one stop along the road. We'll make other stops after Crawford but each stop is built on the positive results of the earlier meetings," said White House press secretary Ari Fleischer.