By Ann Saphir

SAN FRANCISCO (Reuters) - Britain's vote to leave the European Union has thrown financial markets into turmoil and means the U.S. Federal Reserve's ambitions for two rate rises this year have been placed on hold.

The Fed on Friday sought to reassure markets that it would provide liquidity as needed using swap lines in place with other central banks, including the Bank of England as the pound touched a 1985 low against the dollar, world stocks lost more than $2 trillion of their value, and investors rushed for the safety of U.S. Treasuries, pushing the yield on the benchmark 10-year note to a four-year low.

Traders of U.S.-interest rate futures even began to price in a small chance of a Fed rate cut, and now see little chance of any rate hike until the end of next year.

"One can forget about rate hikes in the near term," said Thomas Costerg, New York-based economist at Standard Chartered Bank. "What I'm worried about is that the Brexit vote could be the straw that breaks the back of the U.S. growth picture."

Market volatility in the past year, a stronger U.S. dollar in the past couple of years that has crimped exporters' profits, low oil prices and inflation, and weaker economic growth in U.S. trading partners have kept Fed monetary policy on hold at least twice in the past year.

An interview with Kansas City Fed President Esther George published Friday but conducted before the Brexit outcome was known suggested she still believes U.S. rates need to rise soon.

But comments from other Fed officials in the run-up to the referendum suggest they worried about exactly the kinds of shocks that rippled through financial markets on Friday.

Fed Chair Janet Yellen had warned prior to the vote that Brexit could "negatively affect financial conditions and the U.S. economic outlook".

The question now for the Fed and for central banks globally is how long the shock lasts and how far it spreads. Many investors and economists are worried that the exit vote could stall Europe's faltering growth.

"It depends on how bad things would get and for how long they would stay bad," said Roberto Perli, a partner at Cornerstone Macro LLC and a former Fed staffer. "The problem with trying to handicap outcomes here is that there are too many unknowable unknowns."

A British departure from the now 28-member EU will deprive it of its second-biggest economy and one of the most liberal states, economically.

GLOBAL SENSITIVITIES

Joe Gagnon, a senior fellow at the Peterson Institute for International Economics, had thought the Fed would raise rates once this year.

Brexit, however, will throw the UK into recession, and crimp U.S. exports, payrolls expansion and economic growth by "the equivalent of at least a 25 basis point hike" in Fed interest rates. "It could mean no rate hikes this year," Gagnon said.

If the slowdown deals a severe blow to Europe, which in Gagnon's view is a less likely outcome, the Fed could be forced to delay interest rate rises further.

Global events have repeatedly stayed the hand of the Yellen Fed, which is already loath to do anything to curtail what has been a modest recovery from a deep recession in 2008.

In late 2015 the Federal Reserve deferred an expected interest rate rise after global markets swooned in response to an unanticipated slowdown in China's economy.

Earlier this year, Fed officials cited tighter financial conditions brought on by further heightened worries about China as another reason for caution.

Still, few economists expect the United States to tip into recession as a result of this week's vote. And if growth in U.S. employment, wages, inflation and overall economic output continues, the Fed will need to raise interest rates at some point, even though the full impact of Brexit won't be known for years.

"(Fed policymakers) can’t just put policy on hold for several years – that’s not going to happen," Gagnon said.

(Additional reporting by Jonathan Spicer; Editing by David Chance and Andrea Ricci)