The decision to visit what is one of Glasgow's twin cities has been criticised by some members of the lesbian, bi-sexual, gay and transgender community, unhappy about the country's tough anti-gay laws.
But Mrs Docherty revealed the trip has the backing of leading LGBT campaigners.
The Lord Provost met with senior representatives last month to find out their views about the visit and the views of the wider community.
She described the meeting as "hugely positive" and said the overwhelming consensus was that she should travel to Russia to raise her concerns.
Mrs Docherty had already vowed to highlight Glasgow's unhappiness about the legislation with her counterpart Mayor Michael Chernyshev.
Bruce Fraser, chief executive of Gay Men's Health, said: "I think it is important the Lord Provost doesn't cancel the trip. It is important she goes, otherwise she is cutting off the dialogue."
Robert McKay, national director of the Terence Higgins Trust, added: "It is far more productive and constructive to have a dialogue.
"It gives the Lord Provost an opportunity to discuss the wider issues - how people live with HIV and how they are supported."
Hugh Torrance, youth work director of LGBT Youth, said: "The overwhelming view was that it would be much more powerful for Mrs Docherty to be there and raise these issues.
"It is absolutely the right thing for dignitaries, athletes and anyone travelling there to apply any pressure they can on Russia."
Mrs Docherty pointed out the city had been twinned with Rostov-on-Don for 27 years including a period during the Cold War.
She said: "My predecessors obviously believed - and I agree with them - that the positive way to influence policy is to remain within our partnership. As Lord Provost and First Citizen of Glasgow, my job is to promote Glasgow at home and abroad and on occasion, raise human rights issues.
"It is not practical for cities, countries or states to dissolve long-standing and beneficial relationships because one party does not agree with another's stance on an issue.
"I have written to the Mayor of Rostov on Don and made my position clear on the country's anti-gay legislation.
"What message would breaking up our partnership give gay people in Russia?"