New York (CNN) Russia and China challenged the United States' global leadership in United Nations speeches peppered with bare-knuckled criticism of the Trump administration's hostility toward Iran, its "military hysteria" over North Korea, and its approach to the rest of the world.

The foreign ministers used the backdrop of President Donald Trump's first turn on the world stage to try to cast their countries as standard-bearers of a peaceful, democratic and reasoned approach to global affairs. And they used the opportunity to argue that globalization, technology and emerging markets are bumping the United States off its superpower pedestal.

"The process of creating a polycentric world order is an objective trend," said Russian Foreign Minister Sergei Lavrov, adding a bit of snark. "This is something that everyone will need to adapt to, including those who are used to lording it over others."

China's minister for foreign affairs, Wang Yi, was a little more diplomatic. "We live in an era that's defined by a deepening trend toward a multipolar world," he said, describing a world "that is witnessing profound changes in the international landscape and balance of power."

"Countries can be equal"

He called for the UN to be at the center of the world order, "so countries can be equal, so countries can run global affairs together."

Lavrov, speaking in the aftermath of Russia's attempts to disrupt the US election through a series of cyber-hacking attempts, made a straight-faced appeal for "rules of behaving responsibly in the digital sphere," adding, "We prepared a draft of the universal convention on counteracting cybercrime including hacking."

Trump said on Twitter in July that he and President Vladimir Putin have discussed the creation of a US-Russian cybersecurity unit, an idea that provoked howls of protest from Democrats and others deeply concerned over ongoing investigations into allegations of links between Russia, the Trump campaign, and a President who repeatedly said he wanted better relations with Moscow.

Relations since Trump moved into the White House have been strained, but Lavrov said Russia had been pleased by parts of Trump's first address to the UN, which analysts say Russians saw as acknowledging the need for the US to share the world stage and avoid interference in other countries' affairs and the impulse to dictate what they should do.

Trump, speaking to the General Assembly on Tuesday, liberally sprinkled his remarks with the word sovereignty, saying it should be the basis of international relations and collective action -- though he indicated he would not respect the sovereignty of countries he dislikes, including Venezuela, North Korea and Iran.

"We are pleased to see the President of the United States, Donald Trump, the day before yesterday, from this rostrum, unilaterally say that it's important to abide by sovereignty (in) international affairs; that it is important to lead by example rather than dictate one's will to other people; that countries with different values, culture, and aspirations cannot just co-exist, but they can work side-by-side on the basis of mutual respect, and I think this is something we can all subscribe to," Lavrov said.

Beyond that, Lavrov had few kind words for the US. He condemned what he called "a very dangerous confrontation spiral around DPRK," the acronym for the Democratic People's Republic of Korea, and alluded to Trump's rhetoric about the rising nuclear threat from Pyongyang.

In the weeks leading up to the UN General Assembly, Trump threatened to bring "fire and fury" down upon North Korea if it threatened the United States or its allies. And in his address to the UN, Trump drew dismayed laughter and later, criticism for his declaration that if North Korea threatens the US, he will "totally destroy" it.

"Military hysteria is not just an impasse, it's a disaster," Lavrov chastised, adding that Russia "resolutely condemned the missile adventures of Pyongyang in violation of Security Council resolutions."

Wang reminded everyone that UN Security Council members "must hold an exemplary role" and stress "dialogue over confrontation."

The Chinese minister noted that during the "Six Party" talks between South Korea, China, the US, Russia, North Korea and Japan in 2005, the "US undertook to normalize relations with DPRK." "We call upon the US to honor its former commitment and we call on all parties to play a constructive role in easing tensions," said Wang, who added that, "negotiation is the only way out."

The Chinese minister said his country "will stay firmly committed to the denuclearization of the Korean peninsula," and added, "China is always a force for peace." It was a theme that Lavrov struck as well, presenting Russia, which invaded and annexed Crimea in 2014, as a force for balance, stability and peace on the world stage.

The same, he hinted, could not be said of the United States. "Unfortunately, the arsenal of many Western states have not diplomacy but rough pressure," he said, expanding into criticism of the US policy toward Iran and Trump's hints that he will leave the multilateral Joint Comprehensive Plan of Action that constrains Tehran's nuclear program in return for sanctions relief.

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"Using unilateral sanctions above the sanctions imposed by the Security Council is illegitimate and undermines the collective nature of international efforts," Lavrov said. "Everyone is witnessing with alarm today the newer restrictions by the US against Iran. And they happen to be extraterritorial in nature and they threaten the implementation of the Joint Comprehensive Plan of Action, which became one of the key factors of regional and international stability."

And he rapped US treatment of close Russian ally Venezuela, which is in a state of slow collapse as the government ends democratic governance and the populace struggles with widespread food shortages caused by gross economic mismanagement.

In his address to the UN, Trump referred to sanctions the US has levied on the Latin American country and said he was "prepared to take further action." Venezuelan President Nicolas Maduro "has inflicted terrible pain and suffering on good people of his country," Trump said and called for the restoration of democracy there.

Lavrov said that it was "unacceptable to incite to riots ... for the sake of the so-called democratization of Venezuela." The proper way to handle any "domestic conflict" is for the international community "to encourage parties to reach a rational reconciliation and compromise," he said. Ultimatums, he added, "never led to anything good."