* Dollar falls on Fed chair Powell's speech
* U.S.-China tariff talks end with little progress
* Treasurer Morrison to become Australia's next prime minister
* Graphic: World FX rates in 2018 tmsnrt.rs/2egbfVh (Updates headline, lead, news about Powell speech, rates, adds analyst quote, changes dateline to New York)
By Kate Duguid
NEW YORK, Aug 24 (Reuters) - The dollar index fell to a session low on Friday after Federal Reserve Chair Jerome Powell said steady rate hikes are the best way to protect U.S. economic recovery but suggested the Fed funds rate was getting closer to neutral.
His statement that rate hikes are keeping job growth strong and inflation under control was a high-profile endorsement of the central bank's current policy approach after U.S. President Donald Trump criticized the pace of rate hikes this week.
The dollar index was down a quarter of a percent from its position at 10:00 a.m. EST when the speech began, and down more than half a percent over the day. Analysts suggested the currency fell overall because Powell's speech suggested the central bank may be approaching its neutral federal funds rate.
Neutral monetary policy means the federal funds rate has reached an equilibrium where it neither stimulates nor suppresses economic growth. Once interest rates reach an equilibrium, the Fed will cease its rate-hiking path.
"The dollar's reaction is a part of a narrative that was established earlier this week, one that we saw in the minutes, with respect to the Fed making progress towards neutral," Mazen Issa, senior FX strategist at TD Securities in New York, said.
"Specifically, the reference there was that some members had become more uncomfortable with the narrative in the Fed policy statements that policy is still accommodative," Issa said.
The greenback has been buoyed by a new round of tariffs in the escalating U.S.-China trade conflict and the Fed's latest policy meeting minutes which signaled a September interest rate rise. The dollar has benefited from President Donald Trump's protectionist policies and from a flight to quality as geopolitical tensions mount.
U.S. and Chinese officials ended two days of trade talks on Thursday without any major breakthroughs. The discussions ended as a new round of U.S. tariffs kicked in on $16 billion worth of imports from China, followed immediately by reciprocal tariffs from Beijing.
As a safe haven currency, the dollar has benefited from fears of international trade turmoil in recent months.
With the dollar down, the euro jumped 0.84 percent to $1.163, recouping some losses after shedding more than half a percent during the previous session.
The single currency weakened on Thursday after Italian Deputy Prime Minister Luigi Di Maio threatened his party would vote to suspend funding to the European Union next year unless other EU countries agreed to take in migrants.
The Australian dollar gained half a percent on Friday after the ruling Liberal party voted in a new leader. (Reporting by Kate Duguid and Tom Finn Editing by Susan Thomas)