His message comes as 133,000 members of the union walk out over pay on Wednesday (15 March), compounded by parallel action in France.
Speaking to Sky News, Serwotka claimed more than 40,000 civil servants are on minimum wage, with a similar number being forced to use food banks.
Since March last year, he added, the government has offered members a 2% pay rise.
He said the organisation would negotiate with the central authority if "it made a serious offer", with PCS demanding a 10% increase.
"I can tell you that if, after today, the government still won’t talk, later this week we will be announcing a significant escalation of that industrial action which will really see, I think, disruption increase," he reportedly said.
"Because frankly, not getting any pay rises is not an option for the people we represent."
It comes after around 1.8 million passengers were impacted by Border Force strikes in December 2022.
