* Stocks rise in Europe and Asia, lifted by commodities
* Dollar near post-jobs report lows, lifting copper, gold, oil
* Traders rule out June Fed hike, await Yellen speech
By Nigel Stephenson
LONDON, June 6 (Reuters) - Shares rose in Europe and Asia on Monday, helped by commodity stocks as the dollar remained near its lowest in more than three weeks, after surprisingly weak jobs data led investors to push back expectations for an increase in U.S. interest rates.
Wall Street looked set to follow suit and rebound from the declines triggered by Friday's non-farm payrolls data, according to index futures .
Yields on low-risk U.S. Treasuries fell as expectations faded that rates would rise soon, remaining near almost two-month lows touched after Friday's data. Their German equivalents held close to record-low levels.
The focus for traders and investors shifted to a speech on the economy and monetary policy later on Monday by Federal Reserve Chair Janet Yellen, who will appear at the World Affairs Council of Philadelphia at 1630 GMT.
Elsewhere, sterling fell more than 1 percent on the day at one point. Opinion polls published over the weekend showed growing support for Britain's voting to leave the European Union in a June 23 referendum.
The pan-European FTSEurofirst 300 stocks index gained 0.2 percent, having fallen around 1 percent on Friday. Britain's FTSE 100, which includes several major mining and oil and gas companies, rose 1 percent.
The STOXX 600 basic resources index was up 3.5 percent. Anglo American rose 8.5 percent and Rio Tinto 6.3 percent.
"The mining sector is bouncing up on the back of the weaker dollar," Hantec Markets' analyst Richard Perry said.
The price of copper reached a four-week high. Brent crude oil rose above $50 a barrel.
MSCI's broadest index of Asia-Pacific shares outside Japan rose nearly 1 percent. Australia's mining-heavy S&P/ASX 200 index closed up 0.8 percent.
However, a stronger yen against the dollar helped push Japan's Nikkei stock index down 0.4 percent.
The dollar, which suffered its biggest one-day drop against a basket of major currencies in four months on Friday, recovered some of the lost ground on Monday, rising 0.1 percent.
After dropping to a one-month low of 106.35 yen on Friday, the dollar rose 0.5 percent to 107.08 yen. The euro fell 0.2 percent to $1.1343 per euro.
"Rate hike expectations for June have disappeared. And while the focus has shifted to July, we expect the dollar to be rather subdued this week, with not much of economic data out of the U.S.," said Yujiro Goto, a currency strategist at Nomura.
Sterling fell 0.8 percent to $1.4409, having earlier fallen more than 1 percent to a low $1.4350 on the polls showing increased support for "Brexit".
U.S. 10-year yields, which fell to 1.697 percent, their lowest in almost two months, on Friday, stood at 1.721 percent, up 1.7 basis points.
German 10-year Bunds, the benchmark for euro zone borrowing costs, rebounded to 0.78 percent, up 0.5 bps. They fell as far as 0.065 percent on Friday, their lowest in more than a year, and remained close to a record low of 0.05 percent hit in April 2015.
The British opinion polls and gains by the anti-establishment 5-Star Movement in weekend Italian municipal elections also supported Bunds.
"We have a poll showing the leave camp in the lead in the UK and in Italy we see the 5-Star Movement gaining ground, so political risk is a key issue," said KBC strategist Piet Lammens.
Italian 10-year yields rose 6.6 bps to 1.41 percent after the electoral setback for the government.
Brent crude last traded at $50.21 a barrel, up more than 1 percent on the day, also helped by attacks on Nigerian oil infrastructure. (Additional reporting by Lisa Twaronite in Tokyo, Anirban Nag, Dhara Ranasinghe, Alistair Smout and Sudip Kar-Gupta in London; Editing by Larry King)