Varnish voiced allegations of sexism after being dropped from the Great Britain team, telling the Daily Mail on Saturday that technical director Shane Sutton had told her to “go and have a baby”.
Sutton has denied making the comments and British Cycling insists Varnish’s removal from the programme was on performance grounds.
Varnish, who failed to qualify for the Olympics in the two-woman, two-lap team sprint alongside Katy Marchant, has been invited to meet the equalities officer of British Cycling to discuss her concerns.
Armitstead was reluctant to discuss the situation, because, as a road racer based in Monaco, she is detached from British Cycling headquarters in Manchester and the track team.
“Any athlete in her position has the right to say what she said,” Armitstead said at a Wattbike event in London.
“She’s worked so hard to be in the position she’s in and to have that taken away from her, if she feels that it’s unjust, then she should speak out about it.”
Olympic team pursuit gold medallist Joanna Rowsell Shand expressed surprise at the comments and insisted the women’s and men’s endurance squads were treated equally.
“I was surprised by the comments,” said Rowsell Shand.
“I’ve always thought as a track rider it’s very equal. Compared to the men’s team pursuit squad, we definitely get equal treatment.”
Armitstead discussed gender inequalities within cycling - there remains a large disparity in profile, pay and prize money of men’s and women’s road events - after becoming Britain’s first medallist of London 2012, when she claimed silver in the road race on The Mall.
The 27-year-old won the world title last September and in August will bid for Olympic gold in Rio, but has often had to plough a lone furrow.
“I haven’t operated within British Cycling for a very long time,” Armitstead said.
“I’ve had to forge my own path, because I needed to.”
Armitstead earlier joked about her friendship with Rowsell Shand, who will bid for a second team pursuit Olympic title in Rio this summer.
“It’s nice for Jo to be able to ring up and have a good moan about British Cycling, because I know what it’s like... whoops!” Armitstead joked.