The U.S. central bank will also reduce the size of its asset stock pile by about $1.4 trillion over the next several years as it seeks to restore a normal environment for monetary policy, according to the poll of Wall Street's top banks taken after the Fed's latest policy meeting, which ended on Wednesday.

The rate hike estimates from the primary dealers, the banks authorized to transact directly with the Fed, largely match the projections offered by policy makers themselves for the path of monetary policy. Earlier on Wednesday, the Fed left interest rates unchanged but signaled it still expects one more increase by the end of the year despite a recent bout of low inflation.

The Fed, as expected, also said it would begin in October to reduce its holdings of U.S. Treasury bonds and mortgage-backed securities acquired in the years after the 2008 financial crisis.

The median projection by primary dealers for the federal funds rate by year end was a range of 1.25 percent to 1.50 percent, up from the current 1.00 percent to 1.25 percent and unchanged from a similar survey in July. Fifteen of the 17 banks responding to the survey expect a rate rise by the Fed's final meeting of the year in mid-December, while two saw no change.

Looking into 2018, the median forecast among dealers in the survey sees the Fed proceeding with three more hikes that will lift its benchmark rate to a range of 2.0 percent to 2.25 percent, also in line with the previous survey result.

As for the Fed's nearly $4.5 trillion balance sheet, the dealers see the central bank chopping that down to about $3 trillion. Estimates ranged from a low of $2.5 trillion to as high as $3.4 trillion when the Fed completes what it has called the normalization of its balance sheet.

The portfolio currently is dominated by some $4.2 trillion of U.S. Treasury and mortgage-backed securities acquired in a bid to restrain long-term interest rates and support the economy's recovery from the 2007-2009 global financial crisis.

Before the crisis, the Fed held about $800 billion of assets, most of it Treasuries and no mortgage-related debt. It accumulated mortgage-backed securities with the goal of supporting a recovery in the housing market by helping to keep rates on home loans low.

Policy makers have expressed a desire to return to a Treasury-only portfolio, and a majority of the primary dealers see that as the eventual outcome. Eight of the 14 dealers responding to a question on the matter said the Fed would allow all of its MBS holdings to mature and roll off the portfolio. Five said it would still retain a small number of mortgage bonds and one said he was unsure.

(Reporting by Richard Leong, Saqib Ahmed, Caroline Valetkevitch, Lewis Krauskopf, Karen Brettell and Gertrude Chavez; Writing by Dan Burns; Editing by Chizu Nomiyama)