By Stefano Rebaudo

May 19 (Reuters) - The U.S. dollar strengthened on Tuesday as investors focused on a possible hawkish shift by the Federal Reserve to curb energy-driven inflation, while uncertainty over a potential peace deal in the ‌Middle East also weighed on sentiment.

U.S. President Donald Trump said on Monday there was now a "very good chance" of ‌reaching a deal limiting Iran's nuclear programme. However, the terms of Tehran's latest peace proposal as described in the Iranian reports appeared little changed from Iran's previous ​offer, which Trump rejected last week as "garbage".

The dollar jumped in March after Iran's effective closure of the Strait of Hormuz pushed oil prices higher, weighing on oil-dependent economies such as Japan and the euro zone while increasing safe-haven demand for the U.S. currency.

Oil prices fell 2% on Tuesday after Trump's remarks.

"If tangible progress (in negotiations between Iran and the U.S.) fails to materialise in the coming days, the dollar index could ‌push through 99.50 even without a renewed ⁠military escalation," said ING forex strategist Francesco Pesole.

Analysts argued that the recent rise in U.S. Treasury yields was driven by mounting inflation fears, reinforcing expectations of a shift in Fed policy towards higher interest ⁠rates and a stronger the dollar.

"Even if the Fed moves to signal that it will adopt a neutral bias in June, it may not be enough to stabilise inflation expectations and long-term U.S. Treasury yields," said Thierry Wizman, forex and rates strategist at Macquarie Group.

"An opportunity to change ​the ​Fed's rhetoric decidedly towards 'hawkish' will come with the small flurry of Fed ​speeches between now and June 6."

Investors are now ‌pricing in a 48.5% chance that the Fed could raise rates in December and a 98.8% chance it keeps them on hold at its next meeting in June, the CME FedWatch tool shows.

The U.S. dollar index, which measures the greenback's strength against a basket of six currencies, was up 0.3% at 99.27 after snapping a five-day winning streak on Monday.

The euro was down 0.35% against the dollar at $1.1615.

YEN NEAR INTERVENTION ZONE

Against the yen, the dollar was up 0.20% at 159.18 yen after government data on Tuesday showed that ‌Japan's economy grew by an annualised 2.1% in the first quarter, supporting ​expectations for a Bank of Japan rate increase in June.

Markets are also awaiting ​details of the government’s extra-budget plan, which could further strain ​Japan’s already worsening public finances and weigh on the currency.

Japanese Finance Minister Satsuki Katayama told reporters on ‌Monday that Japan stands ready to act against excessive ​foreign-exchange volatility while ensuring that ​any intervention to support the yen and sell dollars is conducted in a way that avoids pushing up U.S. Treasury yields.

Investors have been on watch for further signs of intervention to support the yen, which is a little stronger than ​before Japanese officials last month began their ‌first foray into the market in almost two years.

The Australian dollar was down 0.75% at $0.7116 after the release of ​minutes from the Reserve Bank of Australia's meeting on May 5. The New Zealand dollar, meanwhile, slipped by 0.6% to $0.5842.

(Reporting ​by Stefano RebaudoEditing by Jamie Freed, Sonali Desai and Gus Trompiz)