SINGAPORE - Asia shares edged cautiously higher on Tuesday while the dollar fell to a six-week low as erratic US trade policies clouded over markets and investors turned defensive ahead of key developments later in the week.

Data on Monday showed US manufacturing contracted for a third straight month in May and suppliers took the longest time in nearly three years to deliver inputs amid tariffs.

"The May ISM showed tariff pressure is beginning to bite for manufacturers who are seeing slowing activity, longer lead times and declining inventories," said economists at Wells Fargo.

The gloomy global trade situation left US futures falling early in the Asian session, failing to sustain the slight gains made during the cash session on Wall Street overnight.

Nasdaq futures and S&P 500 futures were both down 0.2 percent each. In Europe, EUROSTOXX 50 futures advanced 0.28 percent and FTSE futures added 0.15 percent.

MSCI's broadest index of Asia-Pacific shares outside Japan reversed early losses to last trade 0.6 percent higher, while Japan's Nikkei rose 0.66 percent.

Payrolls on deck

The dollar fell to a six-week low against a basket of currencies to 98.58 on Tuesday, ahead of Friday's US nonfarm payrolls data, which will offer a timely reading on the pulse of activity in the world's largest economy.

A rise in unemployment is one of the few developments that could get the Federal Reserve to start thinking of easing policy again, with investors having largely given up on a cut this month or next.

The euro scaled a six-week top earlier in the session before paring some of its gains to last trade at $1.1426, while sterling dipped 0.09 percent to $1.3532.

A softer US jobs report would be a relief for the Treasury market, where 30-year yields continue to flirt with the 5 percent barrier as investors demand a higher premium to offset the ever-expanding supply of debt.

The Senate this week will start considering a tax-and-spending bill that will add an estimated $3.8 trillion to the federal government's $36.2 trillion in debt.

"The evidence suggests term premium being re-priced considerably higher to account for US fiscal, trade, credit, and geoeconomic risks alongside some hedge against (US dollar) debasement," said Vishnu Varathan, head of macro research for Asia ex-Japan at Mizuho.

The dollar was up 0.35 percent against the yen at 143.20, reversing some of its 0.9 percent decline from the previous session.

Bank of Japan Governor Kazuo Ueda said on Tuesday that it is important to make policy judgements without any preset ideas as uncertainty over global tariff policies remains extremely high.

In commodities, oil prices rose on concerns about supply, with Brent crude futures climbing 0.88 percent to $65.20 a barrel, while US crude surged 1 percent to $63.13 per barrel.

Spot gold rose to a roughly one-month high of $3,392.03 an ounce.