* Euro falls as risk sentiment sours
* Yen, Swiss franc both gain
* Fed's cautious comments about economy earlier knock dollar
* Graphic: World FX rates in 2018 tmsnrt.rs/2egbfVh
By Tommy Wilkes
LONDON, Nov 20 (Reuters) - The euro fell from a two-week high on Tuesday as a selloff in European stock markets and nervousness about Italian banks fed through to the currency.
Earlier, cautious comments overnight by Federal Reserve officials about the global economic outlook, weak U.S. data and a selloff on Wall Street had knocked the dollar lower and supported the single currency.
But the euro gave up is gains as European stocks fell, Italian bank shares hit a two-year low and Italian bonds sold off again amid an ongoing confrontation with the European Union over Rome's budget plans.
"It's largely sentiment-driven. European markets have opened weaker and the Italian risk is still in the background and it doesn't help the euro," said Alvin Tan, strategist at Societe Generale.
Developments in the China-U.S. trade conflict, Brexit negotiations and a selloff on Wall Street rattled investors.
The euro fell 0.2 percent to $1.1429 after earlier reaching a two-week high of $1.1472.
With investor nerves high, the safe-haven Japanese yen added 0.2 percent to 112. 33. The Swiss franc gained 0.3 percent versus the euro to 1.1344 francs.
Measured against a basket of its peers, the dollar index rose 0.1 percent to 96.290, off its weakest in two weeks.
The index fell nearly half a percent last week, its biggest weekly drop since late September as investors worry about slowing U.S. economic growth.
Overnight, New York Fed President John Williams said "We will be likely raising interest rates somewhat, but it is really in the context of a very strong economy."
Last week, Fed Vice Chair Richard Clarida and Dallas Fed President Robert Kaplan raised concern over a potential global slowdown, leading markets to bet the rate-hike cycle is near an end, even as the senior Fed officials signalled more interest rate increases.
The Fed executives' remarks led some traders to wonder whether the dollar's rally was ending, with U.S. 10-year Treasury yields pulling back.
Some analysts believe the dollar can stage a comeback, however.
"William's comments are justified but are not as dovish as the comments made by Clarida and Kaplan last week. The market may rethink whether it read Friday's comments as overly dovish, which may lead to a reversal in dollar weakness," said Ray Attrill, head of currency strategy at NAB.
The dollar was also been weighed down by weak housing data on Monday, which pushed down U.S. 10-year bond yields.
U.S. homebuilders' sentiment recorded its steepest one-month drop in more than four years, suggesting that rising borrowing costs are squeezing real estate markets.
The Australian dollar traded lower at $0.7289, pushed lower by fears of Chinese economic slodown. (Additional reporting by Vatsal Srivastava in Singapore, editing by Larry King)