Hunting with dogs could be outlawed for good by 2005, according to Rural Affairs Minister Alun Michael.
Are hunts' days numbered?
He said he would be "very surprised" if people were still fox hunting "in a couple of years time", apart from in exceptional circumstances.
His comments suggest the government has given up all hope of pursuing its compromise deal on licensing some hunting, following Monday night's passionate debate which resulted in MPs voting for an outright ban on the activity.
However, the prime minister's official spokesman later refused to confirm whether Mr Blair would support a bill banning the sport outright.
He said the government had always wanted to find a consensus.
"The bill will have to reflect the vote, but we have to take this one step at a time," he said.
He also refused to be drawn on whether the government would, or could, invoke the Parliament Act to force a ban through the Lords. If it did not take this step, a ban is unlikely to happen.
MPs forced the government's compromise Hunting Bill to become an all-out ban, by 362 votes to 154.
The result sets up another bruising battle with the House of Lords, which has opposed a hunting ban since Labour was elected with a pledge to allow a free vote on fox hunting in 1997.
Ministers dramatically decided at the end of the five hour debate to withdraw an amendment strengthening their compromise bill.
Officials said the government motion was withdrawn as an "act of good faith" because they realised that if had been passed MPs would then not have had the chance to vote on having a complete ban.
Downing Street says it is the Commons speaker who decides the House's business, but critics accuse the government of incompetence.
Ministers have long suggested a total ban would prove "unworkable" and insisted the government's bill was the best way of preventing animal cruelty.
Labour backbencher Tony Banks, who put forward the ban amendment, hailed the vote as "excellent news".
But pro-hunting Labour peer Baroness Mallalieu described Monday night's events as "a fiasco".
Mr Michael said the government decided to drop its amendment after taking the temperature of the Commons debate.
"It was clear that passions went very high and it was quite a large majority that wanted what has been described as a complete ban rather than the option I constructed," he told BBC Radio 4's Today programme.
The bill will now return to a committee of MPs to review the changes, and will not go to the House of Lords until the autumn.
Commons vote was 'a fiasco', says Lady Mallalieu
If the Lords rejects it, MPs would have to pass the bill in two successive sessions of Parliament and then use the Parliament Act to over-ride Lords objections if a ban is to become law.
Mr Michael said he hoped the Lords "would not block" the legislation, but stressed that the government "would not stand in the way" of applying the little-used Parliament Act to force the legislation through.
Asked if he could see hunting continuing in a couple of years, the minister said: "I would be very surprised, other than in the way of exemptions.
"The bill will end up as a ban with exceptions, just as my bill was a ban with exceptions."
But Lady Mallalieu insisted that while the Lords would "not block, not delay" the bill, there was "no way" the Parliament Act could be used to force the measure through.
HUNTING BAN TIMETABLE
1997: Labour's election manifesto promises free vote on a hunting ban
1999: Countryside Alliance marches in support of hunting at Labour Party conference
2000: Burns inquiry says between 6,000 to 8,000 jobs
would be lost by a ban.
2001: Lords votes against Hunting Bill
2002: Six month consultation announced to produce new bill
2003: MPs vote by 362 to 154 to ban fox-hunting with dog
"If an attempt were made to do so... it would be a constitutional outrage," she told Today.
The pro-hunting Countryside Alliance said the vote would only stiffen the resolve of the House of Lords to oppose the ban and "means that a ban on hunting is probably further away, not closer".
But Phyllis Campbell-McRae, the UK director of the International Fund for Animal Welfare, said: "The cruelty of hunting with dogs is unacceptable in modern
society and the vote this evening means that the House of Commons has signalled
a total end to this barbaric activity."