The country’s railway network has been thrown into chaos after the first of the planned strikes on Tuesday and severely reduced services on Wednesday.
The latest talks between RMT union members and railway employers to resolve an ongoing bitter dispute on pay, jobs and conditions broke down earlier this week.
Industrial action continued on Thursday, with more 24-hour strikes planned for Saturday.
Friday and Sunday will also see disruption, with only 60% of trains running, mainly because of delays to the start of services after signallers and control room staff stay away from overnight shifts.
But Mr Lynch said the disruption might not end this week.
He told BBC News talks would continue and he would consult members to see “if and when there needs to be a new phase of industrial action”.
“But if we don’t get a settlement, it’s extremely likely there will be,” he said.
Deputy First Minister John Swinney has previously called for “more urgency” from UK ministers and the Department for Transport (DfT) to alleviate the travel chaos.
About 40,000 Network Rail staff are believed to have walked out at midnight on Tuesday over the ongoing dispute.
ScotRail cancelled 90% of its services, and cross-border services were also badly affected.
The train operator has strongly advised passengers wishing to use their services check updated timetables on their website as the industrial action continues.