By Harry Robertson

LONDON (Reuters) -The dollar bounced on Tuesday after falling to its lowest against the euro, sterling and Swiss franc since mid-March overnight as signs of a softening U.S. economy boosted the case for earlier Federal Reserve interest rate cuts.

Yet the yen powered 0.6% higher for a second day of solid gains as Bank of Japan officials warned they are keeping a close eye on the currency, and a report said the BOJ could soon discuss reducing bond purchases.

The euro was last down 0.4% at $1.0863 on Tuesday after rising as high as $1.0916 for the first time since March 21 in the Asian trading session. It climbed 0.5% as the dollar dropped on Monday.

As the U.S. currency found a footing, the was up 0.27% at 104.32, having fallen to its lowest since mid-April overnight at 103.99.

Data on Monday showed a second straight month of slowdown in manufacturing activity and an unexpected decline in construction spending, causing the dollar index to fall around 0.6%.

“Today’s US JOLTS job openings data could determine whether recent dollar losses are… the start of an important new trend,” said Chris Turner, global head of markets at lender ING.

The U.S. job openings and labour turnover survey (JOLTS) is due out at 1400 GMT, or 10 a.m. ET, and will show the number of vacancies in May. It will also report on the number of people voluntarily quitting their job.

Japan’s yen bucked the trend on Tuesday and continued to rise against the dollar after climbing on Monday, with the U.S. currency down 0.6% at 155.105, around its weakest in two weeks.

Bank of Japan Deputy Governor Ryozo Himino said on Tuesday the central bank must be “very vigilant” to the impact the yen’s fluctuations could have on inflation in guiding monetary policy.

Bloomberg reported that the BOJ will discuss slowing its bond purchases at its two-day policy meeting next week. That could push up yields in the coming weeks and may come before an interest-rate hike in July, something analysts at TD Securities said they now expect on Tuesday.

“We are inclined to see these stories as a test of the market’s reaction rather than anything more concrete, not least given the BOJ’s revealed preference for slow… adjustment,” said Nicholas Rees, FX market analyst at Monex Europe.

Sterling hit its highest since mid-March too at $1.2818 before falling to sit 0.43% lower.

Back in Europe, the dollar fell 0.2% to its lowest against the Swiss franc since mid-March at 0.8938 francs. Data showed Swiss inflation held steady at 1.4% year-on-year in May.

Investors were also keeping an eye on India’s rupee as election results come in, with the currency down on Tuesday amid a lack of clarity about the performance of the alliance led by Indian Prime Minister Narendra Modi.

A number of currencies that have been central to carry trades – whereby investors borrow in countries where interest rates are low and buy the bonds of those where rates are high – saw notable swings on Tuesday.

The high-yielding Mexican peso continued to fall as investors reacted to Claudia Sheinbaum’s landslide victory in Sunday’s presidential election. The low-yielding Japanese and Swiss currencies rallied, while high-yielding sterling dropped.

Also impacting currency markets was a drop in oil prices as investors worried about supply rising later in the year amid signs of weakening U.S. demand.

Australia’s dollar fell 0.8% while Norway’s crown dropped 0.9% in a sign of the currencies of commodity-producing countries coming under pressure.