The mainland Chinese markets ended the day higher by more than 1 percent each. The Shanghai composite rose 1.05 percent to 2,601.73 while the Shenzhen composite advanced 1.399 percent to 1,355.38.
Hong Kong's Hang Seng index gained 1.22 percent in late-afternoon trade.
US-China trade hopes
The two leaders are expected to talk trade after Washington and Beijing applied additional tariffs on billions of dollars' worth of each other's imports. Those moves prompted concerns about slowing global economic growth. Trump and Xi are set to have dinner on Saturday.
Kudlow later told reporters Trump thinks there is a "good possibility" the two countries can reach an agreement. His comments came after the president told The Wall Street Journal that it was "highly unlikely" that the U.S. would delay from increasing tariffs on $200 billion in Chinese goods to 25 percent.
"Markets feel poised for some significant moves and it does look like this G20 meeting is shaping up to be one of the most important in recent history in terms of market focus," said Rakuten Securities Australia in a note. "Of course it's not that actual summit that investors are (focusing) on but the meeting between the President Trump and President Xi and whether we get any positive result for global growth."
"It's unlikely that we will get a concrete agreement between the two sides this week but the market will take any promise of further cooperation as a positive and it will react accordingly," they said.
The sentiment was echoed by a J.P. Morgan executive.
"The two sides are both coming to the table to work out some kind of resolution, even though resolution may be short term but a temporary truce should be positive for markets," Jing Ulrich, managing director and vice chairman of Asia Pacific for J.P. Morgan Chase, told CNBC's "Street Signs" on Wednesday.
Ulrich, however, added the caveat that "we cannot hold out hope that this one dinner will actually end all trade escalation or trade tension forever," even though she said she saw "some kind of light at the end of the tunnel."
Rest of Asia mostly sees gains
In Australia, however, the ASX 200 closed fractionally lower at 5,725.1.
Shares of Australia's major miners were mixed. Rio Tinto fell 2.17 percent and BHP Billiton slipped 0.84 percent while Fortescue Metals Group rose 2.34 percent.
Fed in Trump's crosshairs
During an interview with the Washington Post released on Tuesday, Trump said he thinks the U.S. central bank is "way off-base with what they're doing."
The Post said he blamed the Fed for the recent stock market sell-off and General Motors' plans to close plants and cut more than 14,000 jobs. The president argued that the Fed is hurting the U.S. economy by raising interest rates.
"So the market seems to be jumping at shadows at the moment and against this backdrop of uncertainty the USD remains the prefer(ed) option for weathering the storm," Rodrigo Catril, a senior foreign exchange strategist at National Australia Bank, said in a morning note.
The Japanese yen, widely viewed as a safe-haven currency, was at 113.87 after weakening from levels around 113.4 in the previous session. The Australian dollar traded at $0.7236.
— CNBC's Fred Imbert and Christine Wang contributed to this report.