He also called on all United Nations member states to honour their obligations under Security Council resolutions on sanctions on North Korea.
Washington and Beijing - the North's sole diplomatic and military ally - are working on a new Council resolution targeting Pyongyang, she added.
The test came as global powers engaged in a carrot and stick strategy with North Korea.
The Security Council on Monday condemned the North's latest missile test and warned of new sanctions. The meeting was convened two days after the country test fired a ballistic missile.
Putin said nuclear tests of the type that Pyongyang had been carrying out in recent weeks were unacceptable, but a peaceful solution is needed to ease the ongoing tensions on the Korean Peninsula.
The Council has imposed six sets of sanctions against the North since 2006.
Asked whether North Korea's missile programme was developing faster than expected, he said: "Yes".
U.S. Ambassador Nikki Haley accused North Korea on Tuesday of intimidating the entire worldwide community with its nuclear program, military ability and cyberattacks, and said any country that doesn't implement United Nations sanctions is supporting Pyongyang's actions.
In the statement on Monday, the UN Security Council stressed on the importance of North Korea "immediately showing honest commitment to denuclearization through concrete action".
No draft resolution was circulated to the full council, but Haley said the United States was working with China on a text.
The missile, launched on an unusually high trajectory, flew to an altitude of 2,111.5 kilometers (1,312 miles) and travelled 787 kilometers before landing in the Sea of Japan (East Sea).
"Combining nuclear warheads with ballistic technology in the hands of a volatile leader like Kim Jong-un is a recipe for a disaster", Harris said.
Haley also said that the United States would consider dialog with Pyongyang only if it stopped all nuclear and ballistic missile tests.
"The United States is not past looking at third country entities who are helping North Korea and putting sanctions on them", Haley said.
Speaking to reporters ahead of an emergency meeting of the UN Security Council, Haley vowed to "call out" countries that support Pyongyang and its nuclear ambitions.
"We're not trying to do any of those things", she said.