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

U.S. President Donald Trump and Chinese leader Xi Jinping will likely speak this week, White House press secretary Karoline Leavitt said on Monday, days after Trump accused China of violating an agreement to roll back tariffs and trade restrictions.

The call between the two leaders will be closely watched by markets to see if the tariff-induced blow to global stocks and the dollar this year could get some reprieve or ratchet up, as trade tensions between the world's two largest economies simmer.

Data on Monday showed U.S. 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.

China's factory activity in May also shrank for the first time in eight months, a private-sector survey showed on Tuesday, indicating U.S. tariffs are starting to hurt manufacturers.

The gloomy global trade situation left U.S. 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% each. In Europe, EUROSTOXX 50 futures advanced 0.28% and FTSE futures added 0.15%.

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

"Trump really does have sentiment in the palm of his hands once again," said Matt Simpson, senior market analyst at City Index.

"I suspect we'll hear about 'a really great call' or words to the effect," he said, referring to the expected call between Trump and Xi.

"But we'll need to wait for confirmation from China, who tends to take their time on these matters. Until we get concrete confirmation, price action could be shaky and vulnerable to false breaks...we also have the June 4 deadline for 'best trade deals' from U.S. trading partners to factor in."

In China, mainland markets returned from an extended break on a muted note, with the CSI300 blue-chip index up 0.23% while the Shanghai Composite Index gained 0.3%.

Hong Kong's Hang Seng Index jumped more than 1%, rebounding from Monday's one-month low.

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 U.S. 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% to $1.3532.

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

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 U.S. fiscal, trade, credit, and geoeconomic risks alongside some hedge against (U.S. dollar) debasement," said Vishnu Varathan, head of macro research for Asia ex-Japan at Mizuho.

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

Bank of Japan Governor Kazuo Ueda said on Tuesday 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% to $65.20 a barrel, while U.S. crude surged 1% to $63.13 per barrel. [O/R]

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