By Rocky Swift

TOKYO, April 6 (Reuters) - The dollar crept higher on Thursday but stood near a two-month low as traders weighed how pivotal U.S. jobs data coming out on a stock trading holiday would impact Federal Reserve policy, after a raft of data this week pointed to a cooling economy.

The closely watched U.S. non-farm payrolls report on Friday, when many markets globally are closed, will follow disappointing services sector data from the Institute for Supply Management (ISM) and private employment figures on Wednesday, as well as a slump in U.S. March manufacturing activity at the start of the week.

While the slew of sluggish economic data has caused traders to scale back bets on how much longer U.S. rates would need to stay in restrictive territory, it has simultaneously reignited recession fears.

That has put a lid on risk appetite and sent traders in search of some safe haven assets.

The U.S. dollar index was up 0.14% at 102.01, having slid to a two-month trough of 101.40 in the previous session.

The Japanese yen also found some support from safe haven bids and was last roughly 0.1% higher at 131.20 per dollar.

Meanwhile, the risk-sensitive Australian and New Zealand dollars slid 0.39% and 0.38%, respectively.

"Weak economic data continues to weigh in on investor sentiment, triggering a flight-to-safety bid," analysts at Westpac said in a note to clients.

The risk-averse mood sent U.S. shares lower on Wednesday while Treasuries advanced, which saw the benchmark 10-year yield falling to its lowest since September. Yields fall when bond prices rise.

The 10-year Treasury yield was last at 3.2958%, while the two-year yield, which typically moves in step with interest rate expectations, stood at 3.7605%.

"The key to FX is going to be that interplay between what the what the U.S. economy numbers dish up as far as interest rates and sentiment about Fed policy," said Ray Attrill, head of FX strategy at National Australia Bank.

In other currency action, sterling declined 0.2% to $1.2437, while the euro slipped 0.14% to $1.0891.

The dour economic signs have strengthened the view that the Fed will reverse course on rate increases, with traders hoping for more insight when Federal Reserve Bank of St. Louis President James Bullard speaks later on Thursday.

Cleveland Fed President Loretta Mester, a known hawk, said in an interview with Bloomberg TV on Wednesday that it was too early to know if the Fed would need to raise its benchmark rate at its next policy meeting in early May.

U.S. rate futures markets are currently pricing in a roughly even chance of the Fed leaving rates unchanged at its next meeting, with rate cuts being priced in as early as July and through to the end of the year.

(Reporting by Rocky Swift and Rae Wee; Editing by Edwina Gibbs and Jamie Freed)