Via UNIDIR’s depository of MEWMDFZ documents, I found this 1958 Soviet Proposal to Create A Middle East Zone Free of Nuclear Weapons. Here’s a key excerpt:

The Near and Middle East should and can become a zone of peace, where there are no, and should not be, nuclear weapons and missiles, a zone of good neighbourliness and friendly cooperation between states. The organisers of the Baghdad bloc are trying to prevent this, as indicated during a session of the Council of the Baghdad Pact in Ankara. In connection with the above, the leadership of the Soviet Union considers it necessary to draw the attention of the governments of countries participating in the Baghdad Pact to the fact that all responsibility for such a policy and the consequences arising from it falls on the US government, as well as on the leadership of those countries participating in this bloc that follow the policy of foreign imperialists.