* Asian stocks off to a good start after European rally
* ECB and BOE signal no rush to withdraw stimulus
* U.S. jobs report pivotal for market bets on Fed tapering
Asian stocks rose on Friday, while the euro and sterling nursed losses after the two most important central banks in Europe surprised by assuring investors they were in no hurry to wind down stimulus.
But markets were cautious as they waited for the U.S. jobs report as it could bolster, or derail, the case for the Federal Reserve to start dialling down its asset-buying programme this year. The data are due at 1230 GMT.
MSCI's broadest index of Asia-Pacific shares outside Japan rose 0.3 percent, while Tokyo's Nikkei average gained 1.3 percent.
Australian shares climbed 1.1 percent and their South Korean counterparts advanced 0.7 percent.
"Global markets reacted positively to comments from the European Central Bank (ECB) and this momentum will certainly help the market today," said Kim Young-il, an analyst at Daishin Securities.
Breaking away from its tradition never to precommit on policy, the ECB declared it would keep interest rates at record lows for an extended period and may even cut further. The Bank of England also cautioned investors they were being too quick to bet on higher UK rates.
Those comments lit a fire under European stocks, which posted their biggest one-day jump in 11 months, while UK shares put on their best performance in 20 months.
U.S. stock index futures also rose, indicating that Wall Street could return with a bang after the July 4 holiday.
Currency investors took the central banks' guidance as a green light to sell the euro and sterling, driving both currencies to five-week lows on the greenback.
"The unprecedented adoption of forward guidance by the ECB further increases the divergence in monetary policy versus the prospect of Fed tapering," said Olivier Korber, strategist at Societe Generale.
"The topside risk in euro short rates and therefore in EUR/USD is drastically reduced for the year to come," he wrote in a report, advising clients to keep short euro positions.
The common currency slumped to $1.2883, while the pound slid to $1.5026. That saw the dollar index,, which tracks the greenback's performance against a currency basket, jump 0.7 percent to five-week highs.
The dollar also gained against the Japanese currency, drifting further above 100 yen. It was last at 100.25 yen, near a one-month peak of 100.86 set earlier in the week.
The firmer greenback weighed on some commodity prices that are priced in U.S. dollars. Copper slipped 0.2 percent to $6,935 a tonne, having already fallen 0.6 percent on Thursday. U.S. crude was at $101.36 a barrel, down from a 14-month peak of $102.18.
There is no major economic news due out of Asia on Friday, leaving the focus squarely on U.S. jobs data.