The comments in the Global Times, a popular paper known for its inflammatory rhetoric and hawkish views, came just days after President Xi Jinping called for the eventual global elimination of atomic weapons.
In recent days, Chinese social media has carried pictures purporting to show an advanced intercontinental ballistic missile system deployed in the northeast.
The Dongfeng-41 is reportedly a nuclear road-mobile missile thought to have a payload of 10-12 warheads and a range of 14,000 kilometres (8,700 miles), according to the Global Times.
The paper, a subsidiary of the Communist Party mouthpiece People's Daily, plays to nationalist sentiment and is often believed to channel hardline views within the government.
The Global Times said some media claimed the People's Liberation Army leaked the photos as a warning to Trump.
"They think this is Beijing's response to Trump's provocative remarks on China," it added.
The US president, who took office Friday, has rattled Beijing with tough talk on trade and national security.
On Monday White House spokesman Sean Spicer warned China the US would "defend" American and international interests in the disputed South China Sea, where China has built a series of artificial islands capable of military use.
"If those islands are, in fact, in international waters and not part of China proper, yeah, we'll make sure we defend international interests from being taken over by one country," he said.
Trump's nominee for secretary of state, Rex Tillerson, said last week China's access to the islands might be blocked -- raising the prospect of a military confrontation.
China lays claim to a vast stretch of the waterway within a so-called "nine dash line," including waters claimed by several of its neighbours.
"Even Washington feels that its naval forces and nuclear strength are lacking, so how can China be content with its current nuclear strength when it is viewed by the US as its biggest potential opponent?" it asked.
The paper said China's nuclear forces "must be so strong that no country would dare launch a military showdown" with it.
"China must procure a level of strategic military strength that will force the US to respect it."
The comments were in marked contrast to Xi's speech at the United Nations days earlier.
"Nuclear weapons should be completely prohibited and destroyed over time to make the world free of nuclear weapons," Xi said.
China has been a nuclear power since 1964.
The PLA has been flexing its muscles since Trump's election, showing off upgraded combat aircraft and new fighters. The country's only aircraft carrier entered the Taiwan Strait this month in a symbolic show of strength.
On Monday the PLA navy announced it had commissioned its fifth "carrier killer" guided-missile destroyer and delivered it to the North Sea Fleet.
The system is believed to be designed to deter the US Navy, which has the world's largest number of carriers.
(Except for the headline, this story has not been edited by NDTV staff and is published from a syndicated feed.)