Health Secretary Patricia Hewitt says it is "only a matter of time" before there is a complete ban on smoking in public places in England and Wales.
Patricia Hewitt says almost all of the UK's workplaces could be smoke-free by 2007
Speaking on the BBC's Sunday AM, she did not give a specific timescale, but said a total ban would be "simpler".
But she also defended the current proposed ban, which exempts pubs not serving food and some private clubs.
A total ban is due in Scotland next year, and in Northern Ireland and Wales the year after.
"I've said several times before I think it is only a matter of time before we get to a total ban," she said.
The proposed bans are contained in the Health Bill, due to get its second reading in Commons on Tuesday.
"By the summer of 2007 almost everybody in the workforce, 99% of people, will be in a completely smoke-free environment," Ms Hewitt said.
"But one of the things I find very interesting is that if I look at other countries who've introduced smoking bans, if I look at California, or Australia or France, several other European countries, Norway and so on, all of them did this through two, sometimes three or even four steps.
"In other words they started with a ban that exempted licensed premises or in some cases even the whole hospitality sector. And then as people got used to it and welcomed it, they moved to complete ban," she said.
The government wants to ban smoking in enclosed spaces
Last month there was debate in Cabinet over possibly pushing ahead for a ban without exemptions, but after days of behind-the-scenes argument that proposal was rejected.
Ms Hewitt was asked whether she would be happy if rebel backbench MPs pushed for a total ban by changing the Bill.
"We all of us, all Labour MPs, stood on a manifesto which said we would introduce the ban in exactly the way I have described, in other words a total ban with the exemption for pubs and clubs that don't serve food.
"But what we are also going to do is have a review at the end of three years. We will monitor the impact from day one. And then government will decide."
The chief medical officer Sir Liam Donaldson this week said he had considered resigning over the government's refusal to back his call for a full ban on smoking in public places.
Sir Liam said he decided to stay in place so he could push for smoking in all enclosed public places to be outlawed.
Scotland's public smoking ban, meanwhile, is due to come into force next spring.
The Welsh assembly has voted for an outright ban in public places, and it has won the power to implement it from the UK government by 2007.