* Fed move and rise in risk appetite hit dollar
* But signs risk rally is running out of steam
* Aussie up 0.5%, pound up 0.3%
* Graphic: World FX rates in 2020 https://tmsnrt.rs/2RBWI5E
By Tom Westbrook
SINGAPORE, March 25 (Reuters) - The dollar halted its decline and gains in riskier currencies petered out on Wednesday as fresh rises in coronavirus cases kept markets on edge and the greenback funding market tight.
Foreign exchange markets were in consolidation as the prospect of a huge U.S. stimulus package bolstered Asian stock markets although gains in riskier currencies were tempered.
The safe-haven dollar, which had pulled back from recent peaks, was now steady against the euro EUR= at $1.0789, and fell only marginally against the yen JPY= to 111.11 yen per dollar.
Currencies that fell the hardest last week hung on to overnight gains. The pound GBP=D3 was steady at $1.1759, the Australian dollar AUD=D3 was 0.2% weaker at $0.5941 after running as far as $0.5990 in early trade.
The U.S Federal Reserve's offer of unlimited bond-buying, on top of opening discount dollar funding lines to central banks around the globe, has supported risk sentiment for the past day along with hopes for a huge U.S. fiscal stimulus package.
The Dow Jones posted its biggest one-day gain since 1933 overnight and Asian markets kept the rally going on Wednesday. MKTS/GLOB
But nerves and still-elevated demand for greenbacks in cash capped further gains in currencies like the Aussie, euro and pound.
"It's a nice rebound and we can probably run with it through the Asian session, but whether this mood can hold 24 hours from now, I'm not convinced," said Westpac FX analyst Sean Callow.
"The overall (virus) picture is still very grim and almost certainly going to get worse."
Spain reported its sharpest increase in cases overnight. India announced a 21-day lockdown of its 1.3 billion population. World Health Organization said that New York could become the next epicentre of the pandemic. funding markets, signs of stress remain as businesses and investors drive enormous demand for dollars to cover liabilities and as a shelter from a maelstrom that has hit nearly every asset class.
Cross-currency basis swap spreads, which reflect the cost of borrowing dollars abroad have relaxed for the euro EURCBS3M=ICAP but remain elevated for the yen JPYCBS= and Australian dollar AUDCBS=ICAP , for example.
"There's a lot of reasons to believe that we're not out of the woods yet," said Chris Weston, head of research at Melbourne brokerage Pepperstone.
"People still feel that the downside risk is far more prevalent...this is a traders' market, we're going to get levels where people look to fade this again."
The New Zealand dollar NZD=D3 fell 0.5% to $0.5800, while the Korean won KRW= handed back a small fraction of Tuesday's 3% gain.