By Andrew Galbraith
MSCI's broadest index of Asia-Pacific shares outside Japan extended morning gains and was up 2.5 percent by early afternoon at its highest level since Oct. 10.
Japan's Nikkei stock index was 2.4 percent higher.
U.S. stock futures rose 0.7 percent.
Chinese shares surged and the yuan firmed. Chinese blue-chips gained 3.0 percent, and its start-up board added 3.8 percent, also buoyed by President Xi's pledge on Thursday of more support for private firms.
Bloomberg reported that Trump is interested in reaching a trade agreement with Xi at the Group of 20 nations summit in Argentina later this month and has asked key U.S. officials to begin drafting potential terms, citing people familiar with the matter.
One person said a sticking point in any potential deal is intellectual property theft, where the Trump administration has sought to take a hard line, and it was unclear if Trump was easing up on U.S. demands that China has resisted.
Earlier this week, Trump was quoted as saying Beijing wasn't ready to do a deal and he was prepared to slap more tariffs on China if his meeting with Xi was not productive.
The report came after the two leaders expressed optimism on Thursday about resolving their bitter trade disputes, one of the major factors behind a recent global equity market rout.
Asian shares got off to a strong early start on news of the leaders' phone call and following a stronger close on Wall Street overnight. The Dow Jones Industrial Average and the S&P 500 each gained 1.06 percent while the Nasdaq Composite rallied 1.75 percent.
A combination of bargain-hunting following steep losses in equities last month and some strong corporate earnings have helped power Wall Street's bounce.
After the bell, though, shares of Apple tumbled about 7.0 percent after it said sales for the crucial holiday quarter could miss Wall Street expectations due to weakness in emerging markets and foreign exchange costs.
Apple suppliers in Asia largely shrugged off the news as investors hoped some progress was being made on trade.
Hon Hai Precision Industry Co gained 1.3 percent, and Taiwan Semiconductor Manufacturing Co added 0.2 percent. Tech rival Samsung Electronics Co Ltd also rallied, rising 3.2 percent.
IN THE (DATA) DUMPS
Investors will be looking ahead to a U.S. jobs report, due at 1230 GMT, for more indications on the health of the U.S. economy and the clues on the pace of further interest rate rises.
U.S. nonfarm payroll figures are expected to rise 190,000 in October from 134,000 a month earlier, with average hourly earnings seen increasing 0.2 percent in October after a 0.3 percent gain the previous month.
Those numbers follow data this week revealing slower factory growth around the world, adding to worries about the outlook for corporate earnings, business investment and trade.
Data from the U.S. showed cooling manufacturing activity in October as a measure of new orders hit a 1-1/2 year low. That came after manufacturing surveys showed factory activity and export orders weakening across Asia as the impact of the trade war deepened.
In currency markets, The yuan strengthened to a high of 6.9092 per dollar in onshore markets and also firmed in offshore trade, pulling away from the sensitive 7 level.
The dollar was little changed against a basket of other major currencies.
It gained 0.3 percent against the safe-haven yen to 113.04 yen but otherwise it was under pressure as improved risk sentiment helped to boost other currencies.
The dollar had fallen across the board on Thursday as the pound rallied on reports that London is close to sealing a financial services deal with Brussels, and after the Bank of England hinted at slightly rate rises in future.
"A corrective setup is in place for the USD, with overbought valuations and a series of reversals across various currency pairs arguing for a short-term pullback," RBC Capital Markets analysts said in a note.
The pound stood flat on Friday at to $1.2997.
U.S. crude was flat at $63.68 a barrel. Brent crude was 0.2 percent higher at $73.04.
(Reporting by Andrew Galbraith; Editing by Shri Navaratnam and Kim Coghill)
(This story has not been edited by Business Standard staff and is auto-generated from a syndicated feed.)