LONDON, Sept 4 Reuters The safehaven dollar fell on Monday as risk sentiment improved on hopes China39;s policy stimulus might stabilise the economy, while U.S. jobs data boosted bets the Federal Reserve could be at the end of its rate hike cycle.

With U.S. markets closed on Monday, liquidity is likely to be thin and traders hesitant to place large bets.

The dollar , against a basket of currencies, inched 0.15 lower to 104.08, but remained close to the twomonth peak of 104.44 it touched on Aug. 25. The index gained 1.7 in August, snapping a twomonth losing streak.

China stepped up measures to boost the country39;s faltering economy, with Beijing planning further action including relaxing homepurchase restrictions.

The Chinasensitive euro was up 0.25 at 1.0799, just off a 10week low touched last week against the dollar. The single currency has weakened almost 12 this summer.

The Australian dollar and the New Zealand dollar also got a lift from those measures.

The U.S. dollar is softening against most other G10 currencies today as risk appetite improves on the back of China support measures, said Jane Foley, head of FX strategy at Rabobank.

In the meantime, data on Friday showed U.S. job growth picked up in August, but the unemployment rate jumped to 3.8, while wage gains moderated.

A string of economic data highlighting moderating inflation as well as an easing labour market have added to the impression the U.S. economy is cooling without slowing sharply,…