According to Canadian defense academic Walter Dorn, there such attempts made at the UN by the USSR delegation, but the year is not terribly clearly stated.
At the United Nations, the Soviet Union criticized strongly the U.S. satellite reconnaissance program. At meetings of the both the First Committee and the Committee on the Peaceful Uses of Outer Space (COPUOS, which had been formed in 1959) the Soviet Union campaigned against the use of reconnaissance satellites. They were declared illegal and an intrusion into a sovereign prerogative of States. The Soviets threatened to introduce a draft resolution before a subcommittee of COPUOS, which would condemn the use of spy-in-the-sky satellites. Were it to be adopted these satellites would be "shot down politically."
And that the US pushed back. What that piece does say more clearly is that such objections were notably absent in a later 1963 Soviet speech
On September 9, 1963, the Soviet delegate to the Legal Subcommittee made a speech that was remarkable in that the customary objections to espionage satellites were omitted. There was evidence that the Soviet Union had established a reconnaissance program of its own. This was made apparent when Khruschev, in one of his visits in July 1963, offered to show satellite photos to the Belgian Foreign Minister!
According to a 1962 American paper (pp. 704-705) Soviet academician and space law expert G.P. Zhukov declared in a 1961 conference that US satellites "serve solely aggressive purposes".
Furthermore, in the same year Krasnaya Zvezda declared that specific US satellites like Midas III and Tiros III belonged to that category. Likewise, the somewhat more obscure G. A. Osnitskaya (who also published as A. Galina and who worked at the Soviet Foreign Ministry) said in the same symposium that reconnaissance itself had an aggressive nature.
T. Ganagale in How High is the Sky? more laconically notes that
Soviet jurists such as G.P. Zhukov, G.P. Zadorozhnyj,
G.A. Osnitskaya, and E.A. Korovin advocated the proscription of “space espionage.” [citing]
- G.P. Zhukov, International Status of Cosmic Space, United States Senate Symposium on Legal Problems of Space Exploration, 87th Congress, 1st session, Senate Doc. 26, 1072, 1083 (1961).
- G.P. Zadorozhnyj, The Basic Problems of the Science of Cosmic Law, Cosmos & Int’l L. 23, 53 (1962).
- G.A. Osnitskaya, The Doctrine of International Law and the Conquest of Outer Space, Cosmos & Int’l L. 88, 101 (1962).
- E.A. Korovin, Peaceful Cooperation in Space, Int’l Aff. 61, 63 (March 1962).
Given the positions of many of these apparatchiks [and lack of similar writings later], I'm guessing they were probably unaware of the Soviet plans to launch similar satellites.