Transport minister Graeme Dey should resign if rail strikes go ahead during Cop26, the Scottish Lib Dems have said.
The RMT union is the final holdout in the action, which is set to disrupt the historic summit coming to Glasgow in less than a week.
Up to 30,000 people will descend on Scotland’s largest city over a two-week period and the strikes would hinder their ability to commute to and from the conference hall.
Mr Dey said on Tuesday he was “not optimistic” of a resolution by the deadline, set for 5pm on Wednesday.
He told the BBC’s Good Morning Scotland programme: “This is a situation that we have tried extremely hard to avoid.
“We find ourselves in a perplexing and deeply disappointing situation.”
But union leaders described the offer as “pitiful”, claiming it came with conditions that could cost jobs.
Lib Dem transport spokeswoman Jill Reilly said: “We are talking about delegates from around the world being unable to attend the most important climate summit of all time.
“Hotels in Edinburgh and elsewhere are booked out for this conference but their guests are unsure if they will even be able to reach the venue.
“The travelling public have now had six months of reduced services on the railways, it’s not like this has come out of the blue.”
Ms Reilly went on to point to the resignation of former transport secretary Stewart Stevenson, after a failure to prepare for snow disrupted roads.
“A rail shutdown would be a failure of equal magnitude. If the trains don’t run smoothly and on time for the duration of Cop26, then Graeme Dey should resign.
“The eyes of the world will soon be on Scotland. Ministers need to stop grandstanding and hammer out a deal that gets the trains running.”
Mr Dey added: “RMT keep moving the goalpost.
“If there are strikes during Cop26 then we have to prepare for that.
“Not just to move delegates, but for the wider travelling public who will be disrupted by this.
“We have contingency plans ready and we have to pivot towards implementing those plans in detail, and the deadline tomorrow was simply set to allow everyone to know where we stand so that we can inform the delegates, the travelling public, what will be on offer in the way of services next week.”
In response, RMT Scotland organiser Mick Hogg said the union would be available “morning, noon and night” to resolve the disputes, but added that the comments of the transport minister were “absolutely nonsense”.
“The goalposts were never there to be moved in the first place – we have been stonewalled for the last 18 months,” he said.
“No talks have ever taken place, albeit we’ve been in a dispute for the last eight months on a separate dispute over rest day working where no trains have been running on a Sunday.
“Then all of a sudden because of Cop26 there’s a rush to get around the table in order to find a resolution to the current disputes.”
Mr Hogg added: “We remain available morning, noon and night, anytime, anywhere, in order to get a settlement – that’s our position.”
He said the sticking point was that “efficiency savings”, which he claimed would lead to job losses, were conditions of the most recent offer.