Alun Michael said the government recognised the countryside had gone through "a horrendous time".
"If the message is that the countryside has massive problems, the answer is yes, and we are with you on that," he told BBC Radio 4's Today programme.
But he said the focus of the march, fox-hunting, was an "extremely divisive issue which affects a minority of people".
Threats
And he warned the small number of pro-hunting extremists that "direct action" would not change the "facts, principles and arguments" on hunting.
BBC reporter Robin Chrystal met four pro-hunt supporters in a West Country pub who claimed they were prepared to go to any lengths to protect their way of life.
The men, who refused to give their names, said their entire livelihoods depended on fox hunting.
"If you have a major part of your life taken away what are you going to do?" one of them said on Today.
They threatened to take action against MPs who had homes in the country - "We know where they live," they said.
And they even threatened the prime minister's wife Cherie Blair, who they said, was behind the government's anti-hunting stance.
The next target, they said, was next week's Labour party conference in Blackpool, where they would bring the town to gridlock.
Policing
In response, Mr Michael said: "In a democracy it is ridiculous to think that people can threaten and that that is the means of getting your way.
"I don't think Parliament or Labour MPs will be impressed by being threatened."
Organisers on Sunday's march, the Countryside Alliance, say they are expecting at least 250,000 people to take to the streets.
The parade will be the biggest British civil rights demonstration in living memory and is expected to bring large parts of central London to a standstill for up to six hours.
Those taking part in the protest - called the March for Liberty and Livelihood - are demanding the right to continue fox hunting.
They also want to draw attention to problems they see in rural areas including unemployment, poverty and crime.
Countryside Alliance spokesman Adrian Yalland said: "This march will be a truly global event."
Scotland Yard have committed 1,600 extra officers to police the march.
But Deputy Assistant Commissioner Andy Trotter said he expected it to pass off peacefully.
"We don't need too many police officers because we have had excellent co-operation from the Countryside Alliance," he said.
He warned there would be "considerable congestion" across the whole of the capital.