NEW YORK (AP) - Iran's delegates to the United Nations are confined to a roughly six-block radius of Manhattan, but that hasn't limited their reach as they mount a diplomatic blitz at the UN General Assembly this week.

President Hassan Rouhani has used his time in New York to meet with the leaders of the UK, France, Germany and Japan on the sidelines of the UN meeting. He also met with US media leaders and gave a TV interview to Fox News.

Inside the UN, talk of Iran has made it into speeches by world leaders as the crisis brewing in the Persian Gulf looms over the annual gathering.

But all around, there's been a diplomatic flurry of activity to address the rising tensions, in addition to demonstrations, conversations and interviews all focused on Iran.

It comes as movements of Iran's delegation to the UN are far more restricted than in previous years, when Iranian representatives to the UN were allowed to travel within a 40km radius in midtown Manhattan.

The need for diplomacy and dialogue- both mainstays of the UN- seems to have taken on an added sense of urgency as officials from Europe and the Middle East stress the importance of avoiding escalations that could lead to war.

The sense of urgency follows months of provocations in the Persian Gulf that culminated in a stunning attack earlier this month on key oil facilities in Saudi Arabia.

"We believe that Iran was responsible because these were Iranian weapons," Saudi Arabia's Minister of State for Foreign Affairs, Mr Adel al-Jubeir, told an audience of intellectuals and journalists on Tuesday at the Council on Foreign Relations in New York.

A day earlier, Britain, France and Germany joined the United States and Saudi Arabia in blaming Iran for the Sept 14 attack, even as Iran insists it had no involvement in the strikes that were claimed by Yemeni rebels.

Mr Al-Jubeir described the European statement as a "very significant step forward in terms of the European position".

He said Saudi Arabia wants "to make sure that we avoid war at all costs".

"But we're not going to sit there with our hands tied while the Iranians continue to attack us," he added.

At another gathering that focused on Iran, a senior Gulf official told a small group of reporters in New York earlier in the week that there's still room for diplomacy, but he said the discussion must expand beyond the focus on Iran's nuclear enrichment to include its ballistic missile programme and Teheran's support for Shi'ite militias across the Middle East.

"There is much more room and time for diplomacy and discussions. We must work to engage the US, the Europeans, and the international community in collective diplomacy," the official said, speaking on condition of anonymity because of the sensitivity of the diplomatic efforts.

The current crisis follows President Donald Trump's decision last year to withdraw the US from Iran's nuclear agreement with world powers, reached under the Obama administration.

Mr Trump has since re-imposed and expanded sanctions on Iran, targeting its oil exports and crippling its economy.

In his speech at the UN on Tuesday, Mr Trump reserved his harshest words for Iran, calling it "one of the greatest threats" to the planet.

"All nations have a duty to act. No responsible government should subsidise Iran's bloodlust," he said, accusing Iran of fuelling the wars in Syria and Yemen.

Still, he left open the possibility of a diplomatic breakthrough, saying, "The United States has never believed in permanent enemies. We want partners, not adversaries."

Shortly before Mr Trump took centre stage at the UN General Assembly, Mr Rouhani met with US media leaders and said he'd consider meeting "at any level" to explore what the Trump administration seeks in a new nuclear deal - but not until sanctions against his country are lifted.

There are signs a rapprochement is possible: Pakistan's Prime Minister Imran Khan said on Tuesday he'd begun to mediate between Mr Trump and Mr Rouhani at the US President's request.

Mr Khan provided no details but said he had spoken to Mr Rouhani on Monday after Mr Trump asked Mr Khan to "deescalate the situation".

While diplomatic talks are taking place quietly in different corners of the city, a loud and lively demonstration drew several hundred people to denounce Iran's government just blocks away from the UN headquarters.

The rally's organisers, the Organisation of Iranian American Communities, insisted several thousand people took part in the protest.

Mr Trump's personal lawyer and former New York Mayor Rudy Giuliani addressed the crowd, describing Iran's Supreme Leader Ali Khamenei as "the murdering ayatollah" and Teheran's clerical leadership "the murdering mullahs".

"I am speaking in my individual capacity. I am for regime change. Down with the tyrants in Iran. Down with the ayatollah and the mullahs and all the crooks," Mr Giuliani said.

On Wednesday, as Mr Rouhani delivers his speech to world leaders at the UN, US Secretary of State Mike Pompeo will address a high-level audience of his own at an event organised by the advocacy group, United Against Nuclear Iran.

There, speakers from Israel, Saudi Arabia, Bahrain and the US will gather at a high-end New York hotel to talk more about Iran.