• US Dollar index trims losses as fading hopes for a US-Iran deal revive safe-haven demand.
• Trump says the US must respond after Iran allegedly downed an American helicopter.
• Investors await US inflation data amid mounting speculation over a Fed rate hike.

The United States Dollar Index (DXY) trims earlier losses on Tuesday as traders swing between optimism and caution over a potential US-Iran deal. At the time of writing, the DXY, which tracks the Greenback's value against a basket of six major currencies, is trading around 99.93 after rebounding from an intraday low of 99.68.

Earlier in the day, US President Donald Trump struck an optimistic tone, saying negotiations with Iran were in the "final throes" and that an agreement could be reached within days.

However, market sentiment shifted later after Trump said in a Truth Social post that Iran had shot down a US Apache helicopter patrolling over the Strait of Hormuz. "Nevertheless, the United States must, of necessity, respond to this attack," Trump wrote.

Meanwhile, Israel carried on with military operations in Southern Lebanon despite both sides agreeing to halt attacks, while Iran warned that fighting could resume if Israel continued its "aggression."

The latest developments have tempered hopes for a near-term peace deal between US and Iran. The two sides also remain far apart on key issues, including Iran's nuclear program, the release of frozen assets and Tehran's demand for greater control over the Strait of Hormuz.

As a result, safe-haven demand for the US Dollar remains intact. The Greenback is also finding support from hawkish Federal Reserve (Fed) expectations amid energy-driven inflationary pressures.

Markets now await the US inflation report due on Wednesday. Economists expect the annual headline Consumer Price Index (CPI) to accelerate to 4.2% in May from 3.8% in April. Core CPI is forecast to edge up to 2.9% from 2.8%.

A stronger-than-expected inflation reading would strengthen expectations that the Fed could raise interest rates before the end of the year, offering further support to the USD.

Markets are currently pricing in a 35% chance of a 25-basis-point (bps) rate hike in September, with the odds increasing to 40% for October and 42% for December, according to the CME FedWatch Tool.