Abe expressed congratulations in telephone talks after Putin cruised to victory in Russia's presidential election, giving him at least another six years in power.
"The two leaders confirmed their close cooperation in realising North Korea's denuclearisation" before an expected summit between US President Donald Trump and North Korean leader Kim Jong Un, the ministry said in a statement.
Japan and Russia were both members of the six-party talks, which also involved China, the US and both Koreas.
The talks were designed to offer the North security and economic benefits in exchange for denuclearisation but broke down in 2009 when Pyongyang abandoned them.
Abe and Putin also discussed joint economic activities on disputed islands and "humanitarian measures" for former Japanese islanders, the ministry said.
The Soviet Union seized the islands off Japan's northern coast -- called the Southern Kurils by Moscow and the Northern Territories by Tokyo -- in 1945 in the closing days of World War II.
The two leaders, who have been struggling to make progress on the decades-old dispute, are scheduled to meet in May.
Referring to the poisoning of a former Russian spy in Britain, Abe told Putin that the use of chemical weapons was not acceptable.