The stoppages among conductors and ticket examiners on trains have brought nearly 90 per cent of ScotRail’s trains to a standstill, with only services in and around Glasgow running.
The Rail, Maritime and Transport union (RMT) said its 270 ScotRail train cleaners would also be balloted for strikes.
It threatened to extend ballots to other staff in the dispute over conductors and ticket examiners being paid less than drivers for working on days off.
The union announced the Sunday walkouts by ticket examiners, who mainly work on trains in the Glasgow area, will now continue until July 18.
The strikes have been running every Sunday since April 28, with no trains operating east of Airdrie.
Train conductors, who work across the rest of the ScotRail network, have walked out on Sundays since March 28, which the RMT said could continue until September.
RMT general secretary Mick Lynch said: “RMT ScotRail ticket examiners will be taking strike action again this Sunday and every Sunday for the next two months in their fight for workplace justice and parity between grades.
"Our conductor members are also fully prepared to keep this battle for equality going until the company do the right thing.
“It is a kick in the teeth for these workers that despite their commitment throughout the Covid-19 pandemic Transport Scotland continues to wage war on essential workers who have kept Scotland’s rail services running.
“We are going to be in for a long summer of strike action unless the company gets round the negotiating table with meaningful proposals for resolving the issue of pay equality."
The union said it also planned to hold strike ballots among other ScotRail workers including cleaners, station ticket gate, maintenance and ticket office staff, CCTV operators and train shunters.
RMT Scotland organiser Mick Hogg said: "The words ‘industrial carnage’ spring to mind - created by a managerial attitude that is rotten to the core and is having an adverse effect on our industrial relations.
“The majority of the ScotRail workforce are being treated with contempt and treated differently within ScotRail as the strong view from my members is that we are all key essential workers, not just drivers, and we should be treated equally and valued equally, and not left to fight over the scraps.”
ScotRail described the strikes as “reckless and divisive” in support of a demand for a 50 per cent increase in overtime payments for working no additional hours.
It also accused the union of misrepresenting the situation.
The operator challenged the union’s claims that there was “no weakening of resolve” by pointing out that only a minority of its engineering staff backed strike action in their own ballot.
ScotRail said only 83 of the 167 RMT engineering members eligible to vote supported strike action, which failed the reach the legal threshold required for action to go ahead.
The company said it was facing the most serious financial crisis in its history that involved being given emergency taxpayer support of more than £400 million.
It said that had enabled the Abellio-run firm to protect jobs, with no redundancies, staff furloughed, wages cut, or staff benefits reduced.
It said it “appreciated the hard work of everyone in the railway to keep key workers moving during the pandemic” but “the focus of everyone should be on making the railway an attractive travel option for passengers so we can recover ScotRail, keep people moving, and secure long-term jobs for our colleagues”.
ScotRail operations director David Simpson said: "The RMT union’s strike action during a pandemic is wrong, divisive, and it should be called off.
“ScotRail’s position on 50 per cent overtime pay increases for no additional hours worked will not change in the face of the strike action, given the severe financial challenges we face.
"Now that lockdown restrictions are lifting, we all need to work together to attract more people back to the railway, which is the only thing that will provide long-term job security and give the rail network a sustainable future.
“The reckless actions of RMT bosses are putting railway jobs at risk.”
A spokesperson for the Scottish Government’s Transport Scotland agency, which is in charge of the ScotRail franchise, said: "We fully appreciate the efforts of rail workers in keeping services moving for key workers.
“However, it should be recognised that the Scottish Government has already supported our franchises with around £1 billion, including the emergency measures agreements [to offset revenue loss during the Covid crisis].
"This has ensured every employee has benefited from full pay throughout the pandemic at a time when services and revenue have fallen by up to around 95 per cent.
"In terms of negotiating any change of terms and conditions, collective bargaining rests with the operator and unions concerned.
"However, there is quite simply no additional funding available at this time.
"Any pay increase, including payments for rest day working, would need to be funded by efficiencies agreed through meaningful discussions.
"Given the pressures on public sector finances as a whole, coupled with projections that passenger numbers and revenues won't return to pre-pandemic levels for quite some time, it is only prudent to identify efficiency savings.”
ScotRail is to be taken back into public ownership in March next year for the first time since it became the last British Rail train operator to be privatised 25 years ago.
The decision by Transport Secretary Michael Matheson followed his decision in 2019 to end Abellio’s ten-year franchise three years early following concerns about its performance and the failure to reach agreement over the funding required for the final part of the contract to 2025.