Mick Lynch, RMT union general secretary, said rail bosses “dragged their heels over further talks”, despite the fact the “clock is ticking” to the start of the summit.
Thousands of delegates including world leaders such as US president Joe Biden, will be in Scotland for the crucial climate change talks, which get under way on October 31.
Mr Lynch said he had now written to the First Minister “calling on her to intervene as a matter of urgency to bring about a fair resolution” to the dispute.
In his letter to Ms Sturgeon he said: “It is completely within the Scottish Government’s powers to resolve these disputes before Cop26 commences – it needs to stop stonewalling these key workers and give them the justice, respect and reward they deserve.”
Earlier this week members of another rail union, the TSSA, voted to accept the pay offer from ScotRail.
It comes after Scotland’s railways have seen months of industrial action, with most Sunday services cancelled.
The RMT union meanwhile still plans to strike during the Cop26 climate conference.
Mr Lynch said: “It is frankly disgraceful that rather than getting all parties round the table for meaningful talks to bring about a fair resolution to these disputes, the Scottish Government is still failing to intervene, despite being in control of the ScotRail franchise and having a major interest in the Sleeper service.”
He added: “RMT has made clear from the outset that it is open to meaningful talks.
“Therefore it is disappointing that with the clock ticking and just days to go until COP26, ScotRail and the Sleeper have dragged their heels over further talks, preferring instead to issue inflammatory and misleading communications to its workforce.
“I have therefore today written to the First Minister calling on her to intervene as a matter of urgency to bring about a fair resolution to these disputes.
“As I said in the letter to the First Minister, the Scottish Government needs to stop stonewalling ScotRail and the Sleeper workers and give these green railway workers the justice, respect and reward they deserve.”
However a spokeswoman for Transport Scotland said it was “disappointing” that the RMT had not put the pay offer to its members in a ballot.
She said: “This is a disappointing response from the RMT leadership, particularly as we understand Aslef and TSSA have accepted the pay offer and Unite is recommending it to its members, who they are currently balloting.
“It is therefore disappointing that RMT leadership did not put this very good pay offer to a democratic vote to its members.”
The spokeswoman continued: “In the interest of collective bargaining, we understand that ScotRail would need to re-engage all four unions to determine next steps.
“The RMT leadership has made clear its problem is with rest day working and that would need to be the focus for any further discussions.”
She added: “We are keen to see this issue resolved ahead of Cop26 so everyone who works in Scotland’s railways can play their part in welcoming the world to our country and showcase our efforts towards building a greener, cleaner railway.”