The proposed statement seen by AFP would have demanded that North Korea "conduct no further nuclear tests" and halt missile launches after Pyongyang carried out a failed test on Sunday.
Such statements by the 15-member council have to be agreed by consensus.
Seoul/Beijing: South Korea said on Friday it was on heightened alert ahead of another important anniversary in North Korea, with a large concentration of military hardware amassed on both sides of the border amid concerns about a new nuclear test by Pyongyang.
More than a week earlier, on 8 April, the US Navy announced that a strike group led by the USS Carl Vinson had been diverted north from Singapore to the Western Pacific as speculation mounted that North Korea was preparing a nuclear or missile test.
"It is a situation where a lot of (military) exercise equipment is amassed in North Korea and also a lot of strategic assets are situated on the Korean peninsula because of the South Korea-US military drills", Lee told a briefing.
"We know they have been giving North Koreans components for their nuclear weapons program".
One U.S. official said additional space was also being set aside for aircraft at seven airfields.
Mr Pence said recent US military strikes in Syria and Afghanistan have showed that the resolve of US President Donald Trump should not be tested by Kim Jong-Un.More news: When is the Champions League draw? Can I watch it on TV?
"The eyes of the world are on Beijing", he said. The United States, Japan and South Korea, as well as Russian Federation and China, took part in talks with North Korea on the denuclearization of the Korean peninsula between 2003 and 2009, when Pyongyang withdrew from the talks.
A concept paper circulated to council members ahead of the meeting states that North Korea's "pursuit of weapons of mass destruction represents one of the gravest threats to worldwide peace and security the Security Council faces".
The United States will counter any North Korean attack with an "overwhelming and effective" response, Vice President Mike Pence vowed Wednesday, as he stood on the deck of a massive American aircraft carrier docked in Japan.
North Korean leader Kim Jong Un claimed to be having an upper-hand in the country's stained relationship with USA when a video simulation of a North Korean nuclear missile attack was featured destroying what appears to be an unidentified American city.
Mattis denounced North Korea's attempted missile launch as he began a Middle East tour, telling reporters traveling with him to Saudi Arabia, "the leader of North Korea again recklessly tried to provoke something by launching a missile", he said.
The vice president's comments come after he spoke to USA and Japanese troops on board the USS Ronald Reagan aircraft carrier earlier in the day.
"When we requested to restore the agreed language that was of political importance and expressed commitment to continue to work on the draft. the USA delegation without providing any explanations cancelled the work on the draft", the Russian U.N. mission said in a statement. The U.S. has invited foreign ministers from the 14 other council nations and many are expected to attend.