The presidents of the United States and Iran will both deliver speeches at the United Nations (UN) on Tuesday - as antipathy between the countries deepens.

President Donald Trump is expected to step up his criticism of Tehran in his address in New York, and hours later President Hassan Rouhani will have the opportunity to respond when he steps up to the podium.

Longstanding divisions between the countries have widened under the administration of Trump, who abandoned the 2015 Iran nuclear deal in May and has since sought to put in place a "maximum pressure" campaign on Tehran.

The US president is expected to address relations with the Democratic People's Republic of Korea (DPRK) - at which he lashed out in his UN speech last year - but reserve his toughest language for Tehran.

"You can bet the president will have well deserved strong words for the Iranian regime, which is among the worse violators of UN Security Council resolutions, if not the absolute worst in the world," US Secretary of State Mike Pompeo said at the weekend.

The US accuses Iran of meddling in the Middle East and supporting terror organizations.

Rouhani is expected to stress that Iran is sticking to the 2015 nuclear deal and accuse the US of breaking its international commitments.

Writing in the Washington Post last week, Rouhani said offers of talks from the US were "not honest or genuine" and hit out at Pompeo. He also questioned how the global community could trust the US "while it is threatening to punish other countries for the implementation of the same UN resolution it sponsored and voted for."

The Iranian president has called on the US to return to talks on the nuclear deal and may offer retorts in the manner of his foreign minister, Zavad Jarif, who has repeatedly criticized the US on Twitter.

Adding fuel to the fire is the deadly weekend terror attack in southwest Iran, for which Iran has held "regional terror sponsors and their US masters accountable" according to Zarif.  

US ambassador to the UN Nikki Haley, one of several Iran hawks at the top of Trump's team along with Pompeo and National Security Adviser John Bolton, told CNN that the Iranian leadership should look at its "own home base" over the attack.

Trump will also chair a UN Security Council meeting on Wednesday that is expected to focus on Iran. Rouhani may choose to attend, but he told NBC News on Monday there were no plans for one-on-one talks with Trump.

The Security Council meeting was originally slated to be solely about Iran, but was later broadened to cover nuclear non-proliferation in general in a bid to avoid further isolating the US. In announcing the meeting in a tweet however, Trump only mentioned Iran.

The US "maximum pressure" policy on Iran has been met with fierce resistance from the other JCPOA signatories, who late on Monday reiterated their commitment to the agreement at a meeting on the sidelines of the UN general assembly.  

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EU confirms plan for trade with Iran

What is the Iran nuclear deal?

While Trump is expected to again call for countries to join the US in sanctioning Tehran, the European Unions's (EU) top diplomat Federica Mogherini on Monday confirmed that the bloc is working on a special purpose vehicle that would protect companies from US sanctions including on oil purchases.

Rouhani predicted in his Washington Post article that the opposition to US isolationism would ultimately force the US to "change course once again."

Rising oil prices are one of the fallouts from the US attempts to isolate Iran, with sanctions on oil sales set to roll back in November. With tightened global supply, there are fears that Trump's words in New York could push prices even higher.

"There is an increasing consensus view that supplies are going to get real tight toward the end of the year. It's almost silly season. People are talking about 100 US dollars a barrel. People are making comparison to 2007/2008," John Kilduff, a partner with Again Capital, told CNBC. "There's no real spare capacity. We're very vulnerable and there's no making up Iranian barrels."