By Rae Wee and Alun John

SINGAPORE (Reuters) -The dollar fell on Thursday as share markets hitting record highs drove optimism across asset classes and traders digested a slew of largely better-than-expected business activity surveys looking for implications for interest rates.

Flash Purchasing Managers' Index (PMI) figures showed the downturn in euro zone business activity eased in February as the dominant services sector broke a six-month streak of contraction, offsetting a deterioration in manufacturing.

The euro was last up 0.34% at $1.0856. It rose over 0.5% to its highest in nearly three weeks, after stronger than expected French activity data but dropped back after disappointing German data.

Sterling was up 0.3% at $1.2674, after British PMI data showed the economy kept up its early 2024 momentum, and the yen was steady at 150.26 per dollar.

That left the which tracks the unit against six main peers down 0.3% at 103.67, and on track for a weekly decline of nearly 0.6%, which, if sustained, would be its first week of declines in 2024.

Broad optimism across markets also was weighing on the dollar, which sometimes benefits from market nervousness. Japanese and European share benchmarks both hit record highs on Thursday, in the 's case, surpassing its peak reached back in 1989.

Still, the dollar index is up more than 2% for the year as traders pare back aggressive bets for a slew of rate cuts by the Federal Reserve this year, which has in turn kept the greenback supported.

U.S. business activity data is due later in the day.

"The dollar has come a long way, and the market is taking a breath and doesn't want to put on more dollar longs at this point," said Jane Foley, head of FX strategy at Rabobank.

"What could potentially change that if we have a further build up of that debate about U.S. interest rates, and whether June (for the first rate cut) is realistic, and the next round of U.S. data is going to be instrumental."

"We continue to think that the dollar will get a second wind."

The risk sensitive Australian dollar was up 0.5% at $0.6584, though the traditional safe haven Swiss franc, also strengthened with the dollar down 0.26% at 0.876 francs.

Minutes of the Fed's latest policy meeting released on Wednesday reinforced the message that the central bank is in no hurry to ease rates that officials still expect will begin to be lowered sometime this year.

Traders are currently pricing in just about a 30% chance that the Fed could begin easing rates in May, much lower than an over 80% chance a month ago, according to the CME FedWatch Tool.

That has followed recent data which showed U.S. producer prices and consumer prices rising more than expected in January, alongside persistent strength in the country's labour market.

Elsewhere, the New Zealand dollar hit an over one-month high of $0.6218.

The Reserve Bank of New Zealand (RBNZ) meets next week, and while economists generally expect the bank to hold the cash rate at 5.5%, some see a risk of a hike, which has given some support to the .

"If there is a hike from New Zealand, the market is going to be focused on the argument: 'New Zealand has weak data and is still hiking, the Fed's got resilient data are they going to be cutting," Foley said.