In this edition of the Global Impact newsletter, we look at the host of US officials who have made the trip to China recently, and consider what progress, if any, that has been made in the tense area of US-China relations.

When it comes to exchanges between the United States and China, we’ve all probably got used to their tough talk and fiery rebuttals.

But over the past weeks – even as the rival superpowers remain at loggerheads over a range of issues – it was more about the handshakes and “candid” talks as both sides look towards mending frayed ties.

For a start, July began with a visit to Beijing by US Secretary of the Treasury Janet Yellen, which included meetings with Premier Li Qiang, then-central bank governor Yi Gang and former economic tsar Liu He. She also addressed representatives of American businesses.

Yellen said competition between the United States and China is not a “winner-take-all” scenario, while Beijing urged Washington to remove economic sanctions on Chinese companies and called for joint efforts to address global challenges.

China’s top diplomat, Wang Yi, then met with US Secretary of State Antony Blinken on the sidelines of a regional meeting in Jakarta in mid-July, in what was the second time the pair had met in a month.

While both took the chance to air their concerns and advance their interests, foreign policy observers said the meeting was still useful for reviving communications and rebuilding trust between the two nations.

A few days after the meeting in Jakarta, US climate envoy John Kerry arrived in Beijing and kicked off the first face-to-face negotiations since China suspended cooperation on global warming last year in protest at Nancy Pelosi’s visit to Taiwan.

He first held talks lasting several hours with China’s chief climate negotiator Xie Zhenhua, who offered hope that the two envoys could contribute to improving US-China ties.

The former US secretary of state also met with Wang, who told Washington to adopt a “rational, pragmatic and positive” policy towards China so that the world’s top-two emitters of greenhouse gases could tackle climate change together.

“China is willing to strengthen dialogue and communication with the United States, discuss mutually beneficial cooperation, and jointly address climate change,” Wang said, in an indication that tensions were slightly easing.

Kerry also met with vice-president Han Zheng during the four-day visit but concluded his China tour with no concrete agreements. He told reporters that his engagements had been “long and detailed” and that both countries would work “intensively in the weeks ahead”.

“There are a lot of things that we very clearly agreed on after all this time. But there are also some issues that are going to have to be resolved that are going to take a little more time,” he said.

Some analysts suggested that Kerry’s influence was limited – particularly so as President Xi Jinping told officials at a national conference happening the same time that China’s path towards reducing carbon emissions “must be determined by the country itself rather than swayed by others”.

Kerry wants China to speed up its decarbonisation efforts, but “Xi is not going to want to give any indication that the US can pressure China”, said Scott Moore, director of the Global China Programme at the University of Pennsylvania.

Kerry did not meet the Chinese leader, but another former US secretary of state, Henry Kissinger, did.

The 100-year-old, who helped paved the way for the normalisation of US-China ties, was treated to a lavish lunch and held talks with Xi at the No 5 Villa of the Diaoyutai State Guesthouse – the same place where Kissinger met Chinese leadership during his first China visit in 1971.

Xi told Kissinger that China was willing to explore ways to get along with the US “correctly” and urged the elder statesman to play a constructive role in getting relations back on track.

“We never forget our old friends, nor your historic contributions to promoting the growth of China-US relations and enhancing friendship between the two peoples,” Xi said, referring to the way Kissinger’s initial China trip helped pave the way for President Richard Nixon’s historic visit in 1972.

Kissinger also held talks this month with defence minister Li Shangfu, who had declined earlier meetings with his American counterpart Lloyd Austin, though analysts said the meeting would not be enough to improve military ties between the two nations.

Apart from Kissinger’s surprise visit to Beijing, another major diplomatic development that made headlines in recent days was the abrupt removal of Qin Gang as China’s foreign minister.

Qin has been missing from the world stage since late June, and in a terse statement, China said it was reappointing Wang Yi as its foreign minister. Observers suggested that, even with Qin gone, his combative style of “wolf warrior” diplomacy would likely persist.

There is much to watch in the coming weeks, as it appears that top-level engagement between the US and China is getting back on track.

Blinken is on his Asia-Pacific swing – which includes stops in Tonga, New Zealand and Australia – and his comments will likely be closely parsed by officials in China.

And as Washington mulled further technology curbs, China’s envoy to the US has warned that the country would “definitely” respond and that the government “cannot simply sit idly by”.

But there will likely be more handshakes, too, as US Secretary of Commerce Gina Raimondo plans a trip to Beijing “later this summer”.