The call came just four days after Pyongyang staged its sixth and most powerful nuclear test to date, claiming a "perfect success".
"The international community must unite in applying the greatest possible pressure on North Korea," Abe said in a speech alongside Putin and South Korea's Moon Jae-in at an economic forum in Vladivostok.
"We must make North Korea immediately and fully comply with all relevant UN Security Council resolutions and abandon all its nuclear and ballistic missile programmes in a complete, verifiable and irreversible manner," Abe insisted.
The call came just four days after Pyongyang staged its sixth and most powerful nuclear test to date, claiming a "perfect success" in testing a hydrogen bomb.
The United States on Wednesday demanded the United Nations slap an oil embargo on Pyongyang and a freeze on the foreign assets of its leader Kim Jong-Un in a dramatic bid to force an end to the perilous nuclear stand-off.
Chinese Foreign Minister Wang Yi said Thursday that China would support the United Nations taking further measures against North Korea following its recent test.
"Given the new developments on the Korean peninsula, China agrees that the UN Security Council should respond further by taking necessary measures," he told a press conference in Beijing.
"We believe that sanctions and pressure are only half of the key to resolving the issue. The other half is dialogue and negotiation," Wang added.
Putin meanwhile has repeatedly insisted that further economic pressure on Pyongyang will not work and insisted that the only route is diplomacy.
"It is impossible to intimidate them," Putin said in Vladivostok.
"I am convinced that we can avoid a large-scale conflict including weapons of mass destruction in the region and that we can solve this problem through diplomacy."
US Ambassador Nikki Haley said the United States would be seeking a vote at the council on new sanctions on September 11.
Meanwhile the EU said it is preparing to increase its own sanctions against North Korea, as part of international efforts to punish the rogue state.
"I will put forward to ministers to work in the coming days to increase EU autonomous sanctions," Federica Mogherini said as she arrived for a meeting of EU foreign ministers in Tallinn.
Despite the mounting pressure on leader Kim Jong-Un, the message from Pyongyang remains one of fierce defiance.
North Korea held a mass celebration for the scientists involved in carrying out its largest nuclear blast to date, with fireworks and a mass rally in Pyongyang.
Citizens of the capital lined the streets Wednesday to wave pink and purple pom-poms and cheer a convoy of buses carrying the specialists into the city, and toss confetti over them as they walked into Kim Il-Sung Square.
In a sign of the international stakes over Pyongyang's latest test, China said on Thursday that it had lodged a diplomatic protest with South Korea following its announcement that it would increase deployments of a US anti-missile system.
In a phone call with his Chinese counterpart Xi Jinping, US President Donald Trump on Wednesday insisted that military action against North Korea was not his "first choice" and pushed for a diplomatic option.