* Euro rises for third day
* Italy close to forming govt, announcing PM
* Australian dollar up on renewed risk appetite
* Graphic: World FX rates in 2018 tmsnrt.rs/2egbfVh (Adds quotes, context, updates figures)
By Tom Finn
LONDON, May 14 (Reuters) - The dollar headed for its fourth successive day of losses on Monday as broad risk appetite returned and investors questioned whether a recent rally by the greenback had run out of steam.
The dollar index against a basket of six major currencies hit a 4-1/2-month high last Wednesday, as a rise in U.S. Treasury yields highlighted the wide interest rate gap between the United States and other countries.
But the surge was stymied by soft April U.S. consumer price data published last week that introduced doubts about expectations that the Federal Reserve would raise rates as many as four times in 2018.
The index fell 0.3 percent on Monday to 92.402, backing further away from last week's 2018 peak.
Growing worries about the U.S. budget deficit, which is projected to balloon to more than $1 trillion in 2019 due to a government spending splurge and large corporate tax cuts, have also undermined the dollar along with concerns about the country's current account deficit.
"Barring a significant, and unlikely, pickup in productivity, a persistent USD rally is unlikely as the twin deficits crowd out private investment by raising borrowing costs," said Hans Redeker, global head of currency strategy at Morgan Stanley in London, in a note.
Economists say President Donald Trump's tax cuts and spending plans could backfire by overheating an already strong economy and causing an unwanted pick-up in inflation.
The euro, meanwhile, headed for a third successive day of gains on Monday encouraged by the weaker dollar.
The single currency crept higher even as investors kept a wary eye on political events in Italy.
Italy's anti-establishment 5-Star Movement and the far-right League, both hostile to European Union budget rules, spent the weekend in talks to forge a common policy programme. The parties were adversaries as recently as March but now look likely to form Italy's next government.
The euro gained 0.4 percent to $1.1986, having fallen last week to $1.1823, its weakest since Dec. 22.
"Italian politics aren't a major moving factor in the euro zone yet. It's not an existential threat and isn't driving a lot of positioning," said Manuel Oliveri, an FX strategist at Credit Agricole in London.
"I expect inflation to rebound in the euro zone and that will keep the European Central Bank's stimulus unwinding on track," he said.
A loss of economic momentum in Europe has made policymakers in the euro zone and Britain more cautious about ending the era of extraordinary monetary stimulus.
On Friday, ECB President Mario Draghi said the euro zone needed a new "fiscal instrument" to help weaker member nations if they were being overly penalised by investors during a debt crisis.
Traders pushed out expectations of a rate rise in Britain to end-2018 and in the euro zone to the second half of 2019.
Analysts at ACLS said they expected a reduction in trade tensions between the United States and China to fuel risk-on sentiment this week that would be positive for the Australian dollar and negative for the yen, considered a safe-haven currency.
The Australian dollar rose 0.1 percent to $0.7558 after rallying back from an 11-month low of $0.7413 plumbed on Wednesday.
Investors are focused this week on speeches by Fed and ECB officials, as well as German data on Tuesday that is expected to show some slowdown in economic growth. (Editing by John Stonestreet and David Stamp)