* Dollar falls broadly after Fed cuts 2017, 2018 rate view

* Dollar index hits one-week low

* Oil-linked currencies up as crude prices gain

* Norwegian crown up 2 pct as central bank holds rates steady

(Updates to U.S. trading, new throughout)

By Dion Rabouin

NEW YORK, Sept 22 (Reuters) - The dollar fell to its lowest in a week against a basket of major currencies on Thursday as investors sold the greenback following a writedown of longer-term interest rate expectations from the Federal Reserve.

The Fed left short-term interest rates unchanged at the conclusion of its policy meeting on Wednesday and despite the dissent of three members, who voted in favor of raising rates, the Federal Open Markets Committee largely reduced the number of rate hikes they foresee in 2017 and 2018.

That knocked the dollar almost across the board as investors reduced their expectations for U.S. interest rates.

"On one hand the Fed looks like it will raise rates in December ... and on the surface that's somewhat hawkish and positive for the dollar, but at the same time the Fed lowered its longer-term projected path of interest rates," said Omer Esiner, chief market analyst at Commonwealth Foreign Exchange in Washington.

"It's hard to get too excited about the dollar when the Fed is lowering its projected path of rate hikes into the future."

Higher interest rates make currencies more attractive to investors.

The dollar index .DXY dropped 0.5 percent to 95.189.

The euro EUR= rose to its highest against the dollar in nearly a week, gaining 0.6 percent to $1.1250, while the greenback hit its lowest in two weeks against the Swiss franc CHF= , falling to 0.9663 franc.

With oil prices rising for the second straight day thanks in part to a surprisingly large drop in U.S. crude inventories, oil-linked currencies like the Canadian dollar CAD= , Colombian peso COP= and Russian rouble RUB= all gained against the dollar.

The dollar hit its lowest against the loonie and peso in nearly two weeks and its lowest against the rouble since Aug. 18.

The major mover against the dollar, however, was the Norwegian crown NOK= , which rose more than 2 percent after Norway's central bank left its main interest rate unchanged and suggested further rate cuts may not be needed because of a pickup in the economy.

"The Norges Bank had a meeting today and they sounded much less dovish than what the market had expected," said Charles St-Arnaud, senior strategist and economist at Nomura Securities International in London.

That was despite reports on Wednesday that the country's unemployment rate rose to its highest level in 20 years.

(Reporting by Dion Rabouin; Editing by Meredith Mazzilli) ((Dion.Rabouin@thomsonreuters.com; +1 646 223 5946; Reuters Messaging: dion.rabouin.reuters.com@reuters.net))