The action being considered would go beyond legislation on minimum service requirements on the transport sector which is yet to be introduced despite being mooted years ago.
Downing Street denied the pledge of stronger action was just “rhetoric” or a “negotiating tactic”.
Officials are urgently working on policy options.
The Prime Minister’s official spokesman said: “We want to do it at speed.”
He said the new moves would not affect strike action next week but declined to say whether they could be brought in to impact on walk-outs later this winter.
Tougher anti-strike laws would inevitably raise the level of clashes with unions in the disputes over pay and conditions.
At Prime Minister’s Questions, Mr Sunak said: “Hard-working families right now in this country are facing challenges.
"The Government has been reasonable. It's accepted the recommendations of an independent pay (review) body, giving pay rises in many cases higher than the private sector.
"But if the union leaders continue to be unreasonable, then it is my duty to take action to protect the lives and livelihoods of the British public.
"That's why since I became Prime Minister I have been working for new tough laws to protect people from this disruption."