The positions were announced in a joint document issued after a meeting between leaders Vladimir Putin and Xi Jinping in the Russian capital of Moscow on Tuesday, in which they also condemned Pyongyang's latest missile test as "unacceptable" and urged against "any statements or actions that could lead to an increase in tensions".
"The two sides propose that the DPRK (North Korea) as a voluntary political decision declares a moratorium on testing nuclear explosive devices and ballistic rocket launches, and the US and South Korea refrain from carrying out large-scale joint exercises," the two countries' foreign ministries said in a joint statement.
"Parallel to this, the opposing sides should start negotiations and affirm general principles of their relations including the non-use of force, rejection of aggression and peaceful co-existence," the statement added.
In comments carried by the state news agency TASS, Putin was also quoted as saying: "Our mutual priorities include a comprehensive resolution of the problems of the Korean Peninsula in order to ensure lasting peace and stability in northeastern Asia."
The joint statement followed an announcement by North Korea that it had test-fired its first intercontinental ballistic missile.
The United Nations Security Council will hold an emergency meeting on Wednesday.
UN Secretary-General Antonio Guterres strongly condemned the launch, warning that it "constitutes a dangerous escalation of the situation."
The test also sparked a Twitter outburst from US President Donald Trump, who urged China, North Korea's closest ally, to act to "end this nonsense once and for all".
Beijing has previously called for a "dual-track" approach of "suspension for suspension" that would see North Korea and the US ease up on tensions, and now Moscow has added its weight to the plan.