In an update to MPs, Commons leader Penny Mordaunt did not include the bill among those currently scheduled to be debated before Friday.
Speaking to the BBC in Wales, Mr Sunak declined to say whether the bill would be included.
“I will do everything I can to move these things forward, but it is dependent on the co-operation of other parties,” he added.
The bill only began its journey through the House of Commons last month. It is yet to be debated in the House of Lords, which makes it more difficult for it to be passed quickly.
Under the government’s plan, the age rises were not due to begin until 2027. It would not affect those who can currently buy cigarettes.
It has faced a backlash from Tory MPs, with 58 of them, including some of Mr Sunak’s ministers, voting against it in the Commons last month after the PM granted them a free vote.
Ex-prime minster Boris Johnson has also led Tory opposition outside Parliament, branding the plan “absolutely nuts”.
Source Agencies
