FOREX-Dollar strengthens as investors weigh Fed outlook and Middle East uncertainty

* Investors focus on potential increases to U.S. interest rates

* Oil prices fall after Trump remarks lift peace hopes

* Yen returns to intervention zone close to 160 (Recasts paragraph 1, adds comments)

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 Rebaudo Editing by Jamie Freed, Sonali Desai and Gus Trompiz)