South Korean officials believe more provocation from the reclusive state is possible, despite international outrage over Sunday's test and calls for more sanctions on North Korea.
South Korea's Asia Business Daily, citing an unidentified source, reported on Tuesday that North Korea had been spotted moving a rocket that appeared to be an intercontinental ballistic missile (ICBM) towards its west coast.
The rocket started moving on Monday and was spotted moving only at night to avoid surveillance, the report said.
South Korea's defence ministry, which warned on Monday that North Korea was ready to launch an ICBM at any time, said they were unable to confirm the contents of the report.
North Korea tested two ICBMs in July that could fly about 10,000 km (6,200 miles), putting many parts of the U.S. mainland within range and prompting a new round of international sanctions against Pyongyang.
On Monday, U.S. Ambassador to the United Nations Nikki Haley said North Korean leader Kim Jong Un was "begging for war" and urged the 15-member U.N. Security Council to impose the "strongest possible" sanctions to deter him and shut down his trading partners.
U.S. President Donald Trump held calls with foreign leaders on Monday, including South Korean President Moon Jae-in and German Chancellor Angela Merkel, and the White House declared that "all options to address the North Korean threat are on the table".
South Korea is talking to Washington about deploying aircraft carriers and strategic bombers to the Korean peninsula, and has been ramping up its own defences in the meantime.
Moon and Trump agreed on Monday to scrap a warhead weight limit on South Korea's missiles, South Korea's presidential office said, enabling it to strike North Korea with greater force in the event of a military conflict. The White House said Trump gave "in-principle approval" to the move.
Under the current guidelines, last changed in 2012, South Korea can develop missiles up to a range of 800 km (500 miles) with a maximum payload of 500 kg (1,102 pounds)
South Korea's navy also held more drills on Tuesday.
"Today's training is being held to prepare for maritime North Korean provocations, inspect our navy's readiness and to reaffirm our will to punish the enemy," an unidentified South Korean naval officer told the same Defence Ministry briefing.
"PATIENCE NOT UNLIMITED"
"War is never something the United States wants. We don't want it now. But our country's patience is not unlimited. We will defend our allies and our territory," Haley said.
China, North Korea's main ally and trading partner, and Russia called for a peaceful resolution to the crisis.
"China will never allow chaos and war on the (Korean) peninsula," said Liu Jieyi, the Chinese ambassador to the United Nations, urging North Korea to stop taking actions that were "wrong" and not in its own interests.
Russia said peace in the region was in jeopardy.
"Sanctions alone will not help solve the issue," Russia's U.N. Ambassador Vassily Nebenzia said.
North Korea has been under U.N. sanctions since 2006 over its ballistic missile and nuclear programmes. Typically, China and Russia only view a test of a long-range missile or a nuclear weapon as a trigger for further possible U.N. sanctions.
U.S. Defense Secretary Jim Mattis warned of a "massive" military response if the United States or its allies were threatened in the wake of Sunday's test. Pyongyang said it had successfully tested an advanced hydrogen bomb for a long-range missile on Sunday, something experts believe it has now achieved or is very close to achieving.
Trump has previously vowed to stop North Korea developing nuclear weapons and said he would unleash "fire and fury" if it threatened U.S. territory.
Despite the tough talk, the immediate focus of the international response was on tougher economic sanctions.
Diplomats have said the Security Council could now consider banning North Korean textile exports and its national airline, stop supplies of oil to the government and military, prevent North Koreans from working abroad and add top officials to a blacklist to subject them to an asset freeze and travel ban.
The sanctions imposed after July's missile tests aimed to slash Pyongyang's $3 billion annual export revenue by a third by banning exports of coal, iron, lead and seafood.