The Buran, the Soviet response to the Space Shuttle, was approved on 17 February 1976 by the Central Committee of the Soviet Communist Party and the Council of Ministers of the USSR. The purposes (quoting directly from the decree) were given as

• counteracting the measures taken by the likely adversary to expand the use of space for military purposes
• solving purposeful tasks in the interests of defense, the national economy, and science
• carrying out militaary and applications research and experiments in space to support the development of space battle systems using weapons based on known and new physical principles
• putting into near-Earth orbits, servicing in these orbits, and returning to Earth space vehicles for different purposes, delivering to space stations cosmonauts and cargo and returning them back to Earth...

For your question, the "counteracting the measures" line is the most interesting; the question is, were they implying possible nuke drops from the Shuttle?

There a report by the mathematicians Sikharulidze and Okhotsimsky (from the Institute of Applied Mathematics) which implies the Space Shuttle really did have special capability to drop a payload over Moscow. From Sikharulidze's recent memoirs:

Из проведенного анализа следовал естественный вывод о возможном использовании многоразовой системы «Спейс шатл» для нанесения упреждающего обезглавливающего удара по Москве.

Following the analysis, we formed a natural conclusion about the possible use of the "Space Shuttle" for a pre-emptive strike on Moscow.

The problem is the report came five weeks after the approval, in March. It was meant to justify the decision after it had already been made.

So the report came too late for the Buran to be a "response" to thinking the Americans were using the shuttle to drop nukes, but in a way, the two were still connected; it wasn't too hard for rumors and the historical game of telephone to reverse the order of the two.

(Unfortunately for Sikharulidze and Okhotsimsky, the idea is ridiculous -- their idea involves bombing on re-entry, the Shuttle's flight trajectory was specially designed to avoid Moscow, and it had no door besides that could drop bombs even if they wanted to; the doors are on the top and had to remain closed.)

Sources:

Hendrickx, B., Day, D. (2020, February 3) Target Moscow (part 2): The American Space Shuttle and the decision to build the Soviet Buran. The Space Review.

Сихарулидзе, Ю. Г. (2017). Космические встречи.

Vis, B., Hendrickx, B. (2007). Energiya-Buran: The Soviet Space Shuttle. Germany: Springer New York.