Asian shares firmed on Monday as some semblance of calm returned to bond markets after last week's wild ride, while progress in the huge U.S. stimulus package underpinned optimism about the global economy.

China's official manufacturing PMI out over the weekend missed forecasts, but investors are counting on better news from a raft of U.S. data due this week including the February payrolls report.

Also helping sentiment was news deliveries of the newly approved Johnson & Johnson COVID-19 vaccine should start on Tuesday.

MSCI's broadest index of Asia-Pacific shares outside Japan edged up 0.1 percent, after shedding 3.7 percent last Friday.

Japan's Nikkei rallied 2 percent, while NASDAQ futures bounced 0.8 percent and S&P 500 futures 0.7 percent.

Yields on U.S. 10-year notes came off to 1.4 percent, from last week's peak of 1.61 percent, though they still ended last week 11 basis points higher and were up 50 basis points on the year so far.

"The bond moves on Friday still feel like a pause for air, rather than the catalyst for a move towards calmer waters," said Rodrigo Catril, a senior strategist at National Australia Bank (NAB).

"Market participants remain nervous over the prospect of higher inflation as economies look to reopen aided by vaccine rollouts, high levels of savings along with solid fiscal and monetary support."

Analysts at Bank of America (BofA) noted the bond bear market was now one of the most severe on record with the annualized price return from 10-year U.S. govt bonds down 29 percent since last August, with Australia off 19 percent, the UK 16 percent and Canada 10 percent.

The rout owed much to expectations of faster U.S. growth as the House passed President Joe Biden's $1.9 trillion coronavirus relief package, sending it to Senate.

BofA's U.S. Economist Michelle Meyer lifted her forecast for economic growth to 6.5 percent for this year and 5 percent next, due to the likelihood of the larger stimulus package, better news on the virus front and encouraging data.

Higher U.S. yields combined with the general shift to safety helped the dollar index rebound to 90.917 from a seven-week low of 89.677.

Early Monday, the euro was holding at $1.2086, compared to last week's peak of $1.2242, while the dollar held near a six-month top on the yen at 106.50.

"Riskier" currencies and those exposed to commodities bounced a little after taking a beating late last week, with the Australian and Canadian dollars up and emerging markets from Brazil to Turkey looking steadier.

Non-yielding gold was still nursing losses after hitting an eight-month low on Friday en route to its worst month since November 2016. It was last at $1,737 an ounce, just above a trough around $1,716.

Oil prices extended their gains ahead of an OPEC meeting this week where supply could be increased. Brent gained 4.8 percent last week and WTI 3.8 percent, while both were about 20 percent higher over February as a whole.

Brent was last up 92 cents to $65.34, while U.S. crude rose 97 cents to $62.47 per barrel.