Hong Kong (CNN Business) Asian markets have been see-sawing this week on signals from US-China trade negotiations, and mostly edged up on Friday after fresh signs that the two countries are working to hammer out a deal.

"Asian equities caught a dose of the trade flu at the start of the week and appear to be recovering today," Jeffrey Halley, senior market analyst for Asia Pacific at Oanda, wrote in a note.

The Wall Street Journal reported Thursday that China's top trade negotiator Liu He had invited his US counterparts to Beijing for a new round of face-to-face talks, which Chinese officials hope can take place before next week's Thanksgiving holiday.

earlier in the week, as investors reacted to multiple media reports that the United States and China may not be able to reach a "phase one" deal until next year. President Donald Trump also told reporters on Wednesday that he is not ready to make a deal with China because he didn't think China was "stepping up to the level" that he wanted.

But investor optimism appears to have returned slightly after China's commerce ministry spokesman Gao Feng said on Thursday afternoon that China is willing to work with the United States to tackle the main concerns of both sides to try to reach a deal.

But analysts say an agreement before 2020 is not a given.

"The likelihood of having a deal signed by year-end still looks very uncertain with the slew of mixed news we have had so far," said Jingyi Pan, market strategist at the IG Group.