FOREX-Dollar heads for worst week in a month on weak U.S. data run

* Dollar index on track for worst week in month

* U.S. CPI (Other OTC: CPICQ - news) next focus after series of lacklustre economic data

* FX market appears sanguine on "Grexit" risk

By Jemima Kelly

LONDON, April 17 (Reuters) - The dollar fell for a fourth straight day on Friday, coming close to its one-week low, after a run of weak U.S. economic data cast doubt on prospects for a Federal Reserve interest rate rise in coming months.

The latest data showed U.S. housing starts rose less than expected in March and factory activity in the mid-Atlantic region grew modestly this month. That suggests the economy may struggle to rebound from a weak first quarter.

The dollar index, which measures the dollar's performance against a basket of major currencies, traded 0.3 percent lower at 97.429. It is on track to fall almost 2 percent this week -- its biggest loss in a month.

"The real question for the dollar is: is this just a poor quarter or is this the beginning of a trend of slower data in the States?" said Peter Kinsella, senior FX strategist at Commmerzbank in London.

Benefiting from the dollar's weakness, the euro has had its best week in a month against the greenback. The single currency has risen almost 2 percent, despite growing concern that Greece's debt crisis will lead the country to default and leave the euro zone. It was 0.2 percent higher on Friday at $1.07865 .

"Greece is not an issue for the FX market," Kinsella said. "Every corporate in Europe at this stage has contingency plans in the event of a Grexit. Even (Taiwan OTC: 6436.TWO - news) when it were to take place it wouldn't really be a surprise for the market, so further downside in the euro on that basis is not so obvious."

Traders will watching U.S. consumer inflation data due at 1230 GMT. Soft data could reinforce the view the Fed will delay any rate hikes, said Mitul Kotecha, head of FX strategy, Asia-Pacific for Barclays (LSE: BARC.L - news) in Singapore.

Also watched by the market will be a meeting of Group of 20 finance ministers and central bankers, with a communique and news conference expected around 1700 GMT. Analysts, however, played down the event's potential impact on currencies.

A focal point will be whether any comments express concern about dollar strength, possibly from U.S. officials, Barclays' Kotecha said. "But I suspect that's not going to be the case," he said. (Additional reporting by Masayuki Kitano in Singapore; Editing by Larry King)