According to the statement, North Korea also urged the United States to think of Pyongyang's strategic position, instead of exerting pressure and introducing sanctions against the country.
The South's military has deployed dozens of giant loudspeakers along the tense border to blare out a mix of world news, K-pop songs and other propaganda targeting young North Korean soldiers.
Despite condemning the ICBM test, South Korean President Moon Jae-in on Monday offered talks with North Korea, indicating for the first time since his inauguration in May that he wants to use dialogue to defuse the global standoff over the North's nuclear and missile programs. "The president is fully aware of those", said Gorka.
"This is not a time for dialogue, it's a time for pressure", he said.
China National Petroleum Corp (CNPC), a state-controlled company, halted diesel and gasoline sales to North Korea "over the last month or two", amid worldwide pressure on Pyongyang to curb its nuclear and missile programs, Reuters exclusively reported on June 28.
"Global action is required to stop a global threat".
"It will be a fatal mistake to consider any chance that the DPRK which rose to a dignified nuclear power and an ICBM state would tolerate the reckless "sanctions" racket of the USA and other hostile forces", it said.
"China has always been strictly abiding by the UN Security Council resolutions and related laws to impose sanctions on North Korea", Mr Huang Songping, spokesman for the General Administration of Customs, said at a briefing in Beijing.
No details have been released.
If realized, the talks would be the first inter-Korean dialogue since December 2015.
USA officials have also warned China could face United States trade and economic pressure - something Mr Trump has held in abeyance since taking office in January - unless it does more to restrain its neighbour. But he also stressed that, "we need to see what sanctions are most successful".
The so-called secondary sanctions now being considered are a way for the United States to apply targeted economic pressure on companies in countries with ties to North Korea by denying them access to the USA market and financial system.
The Red Cross said it hoped for "a positive response" from its counterpart in the North, hoping to hold family reunions in early October.
In the wake of the latest test, U.N. Ambassador Nikki Haley is calling for further sanctions against North Korea.
China, North Korea's neighbor and closest ally, is responsible for 90 percent of trade with the country.
He said Russian Federation also has "an extremely important role to play in dealing with the North Korean problem and we will encourage Russian Federation to play some even greater role".