China has said it is cancelling or suspending dialogue with the United States on a range of issues from climate change to military relations and anti-drug efforts in retaliation for a visit this week to Taiwan by US House of Representatives speaker Nancy Pelosi.

The measures, which come amid cratering relations between Beijing and Washington, are the latest in a promised series of steps intended to punish the US for allowing the visit to the island it claims as its own territory, to be annexed by force if necessary.

The White House summoned China’s ambassador to protest against what it called China’s “irresponsible” actions since the visit.

China on Thursday launched threatening military exercises in six zones just off Taiwan’s coasts that it says will run until Sunday.

Missiles have also been fired over Taiwan, defence officials told state media.

China opposes the self-governing island having its own contacts with foreign governments, but its response to the Pelosi visit has been unusually vociferous.

The Foreign Ministry said dialogue between US and Chinese regional commanders and defence department heads would be cancelled, along with talks on military maritime safety.

Co-operation on returning illegal immigrants, criminal investigations, transnational crime, illegal drugs and climate change will be suspended, the ministry said.

China said on Friday that more than 100 warplanes and 10 warships have taken part in the live-fire military drills surrounding Taiwan over the past two days, while announcing mainly symbolic sanctions against Ms Pelosi and her family over her visit to Taiwan earlier this week.

The official Xinhua News Agency said on Friday that fighters, bombers, destroyers and frigates were all used in what it called “joint blockage operations”.

The military’s Eastern Theatre Command also fired new versions of missiles it said hit unidentified targets in the Taiwan Strait “with precision”.

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A military fighter jet flies above the Taiwan Strait (Ng Han Guan/AP)

The Rocket Force also fired projectiles over Taiwan into the Pacific, military officers told state media, in a major ratcheting up of China’s threats to attack and invade the island.

The drills, which Xinhua described as being held on an “unprecedented scale”, are China’s most strident response to Ms Pelosi’s visit. The speaker is the highest-ranking US politician to visit Taiwan in 25 years.

Dialogue and exchanges between China and the US, particularly on military matters and economic exchanges, have generally been halting at best.

Climate change and fighting trade in illegal drugs such as fentanyl were, however, areas where they had found common cause, and Beijing’s suspension of co-operation could have significant implications for efforts to achieve progress in those issues.

The two countries’ top climate diplomats, John Kerry and Xie Zhenhua, maintained a cordial relationship that dated back to the Paris climate accord, which was made possible by a breakthrough negotiated among the two and others.

China under Mr Kerry’s prodding committed at last year’s UN global climate summit in Glasgow to working with the US “with urgency” to cut climate-wrecking emissions, but Mr Kerry was unable to persuade it to significantly speed up China’s move away from coal.

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Nancy Pelosi with Taiwan’s Foreign Minister Joseph Wu as she arrived in Taipei (Taiwan Ministry of Foreign Affairs via AP)

On Friday morning, China sent military ships and war planes across the mid-line of the Taiwan Strait, the Taiwanese Defence Ministry said, crossing what had for decades been an unofficial buffer zone between China and Taiwan.

Five of the missiles fired by China since the military exercises began on Thursday landed in Japan’s Exclusive Economic Zone off Hateruma, an island far south of Japan’s main islands, Japanese Defence Minister Nobuo Kishi said. He said Japan protested the missile landings to China as “serious threats to Japan’s national security and the safety of the Japanese people”.

Japan’s Defence Ministry later said they believe four other missiles fired from China’s south-eastern coast of Fujian flew over Taiwan.

Japanese Prime Minister Fumio Kishida said on Friday that China’s military exercises aimed at Taiwan represent a “grave problem” that threatens regional peace and security.

Chinese Foreign Ministry spokesperson Hua Chunying said China’s actions were in line with “international law and international practices”, though she provided no evidence.

“As for the Exclusive Economic Zone, China and Japan have not carried out maritime delimitation in relevant waters, so there is no such thing as an EEZ of Japan,” Ms Hua told reporters at a daily briefing.

In Tokyo, where Ms Pelosi is winding up her Asia trip, she said China cannot stop US officials from visiting Taiwan.

Mr Kishida, speaking after breakfast with Ms Pelosi and her congressional delegation, said the missile launches need to be “stopped immediately”.

China said it summoned European diplomats in the country to protest statements issued by the Group of Seven industrialised nations and the European Union criticising the Chinese military exercises surrounding Taiwan.

Its Foreign Ministry on Friday said Vice Minister Deng Li made “solemn representations” over what he called “wanton interference in China’s internal affairs”.

Mr Deng said China would “prevent the country from splitting with the strongest determination, using all means and at any cost”.

The ministry said the meeting was held on Thursday night but gave no information on which countries participated. Earlier on Thursday, China cancelled a foreign ministers’ meeting with Japan to protest the G7 statement that there was no justification for the exercises.

Both ministers were attending a meeting of the Association of Southeast Asian Nations in Cambodia.

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Secretary of State Antony Blinken (Andrew Harnik/AP)

China has promoted the overseas support it has received for its response to Ms Pelosi’s visit, mainly from fellow authoritarian states such as Russia, Syria and North Korea.

China had earlier summoned US Ambassador Nicholas Burns to protest against Ms Pelosi’s visit. The speaker left Taiwan on Wednesday after meeting with President Tsai Ing-wen and holding other public events. She travelled on to South Korea and then Japan. Both countries host US military bases and could be drawn into a conflict involving Taiwan.

The Chinese exercises involve troops from the navy, air force, rocket force, strategic support force and logistic support force, according to Xinhua.

They are believed to be the largest held near Taiwan in geographical terms and the closest in proximity — within 12 miles of the island.

US Secretary of State Antony Blinken on Friday called the drills a “significant escalation” and said he has urged Beijing to back down.

US law requires the government to treat threats to Taiwan, including blockades, as matters of “grave concern”.

The drills are an echo of the last major Chinese military drills aimed at intimidating Taiwan’s leaders and voters in 1995 and 1996.

Taiwan has put its military on alert and staged civil defence drills, but the overall mood remained calm on Friday. Flights have been canceled or diverted and fishermen have remained in port to avoid the Chinese drills.