The world is "looking away as genocide is committed" in Darfur, says Northern Ireland Secretary Peter Hain.
Hugh Grant is one of a number of celebrities to support the action day
The minister was speaking ahead of a global day of action about the conflict in the Sudan region, which will include a protest outside 10 Downing Street.
Tory Andrew Mitchell, who will speak at the London rally, said it was "shameful" the world had not "turned the screws on the bullies in Khartoum".
An estimated 200,000 people have been killed in the four-year conflict.
Celebrities including Hugh Grant, Bob Geldof and Mariella Frostrup have joined the calls for world governments to act to end the bloodshed.
Protesters at Downing Street on Sunday will urge the UK government to keep pushing for an effective peacekeeping force in the region.
Mr Mitchell, who is shadow international development secretary, said Tony Blair should take the lead in the final days of his premiership.
"We need to enforce targeted sanctions against the regime's leaders by freezing their bank accounts and applying travel bans to stop their shopping trips to Paris and London," he said.
But the top priority should be ending the violence with a "better equipped and better mandated international force", he said.
Liberal Democrat spokeswoman Lynne Featherstone accused the government of doing nothing and demanded an arms embargo and "meaningful sanctions".
More than two million people are living in camps after fleeing fighting in the region.
The African Union (AU) peacekeeping force is struggling to halt widespread abuses and violence, but Sudan is rejecting plans for it to hand over to a larger, stronger UN mission.
Sudan's government and the pro-government Arab militias are accused of war crimes against the region's black African population, although the UN has stopped short of calling it genocide.
As part of the day of action demonstrators will turn round some 10,000 hourglasses filled with fake blood, under the slogan "Time is up... protect Darfur".
'Enough is enough'
Former child soldier turned musician Emmanuel Jal will speak at the London event.
Ismail Jarbo, a survivor from Darfur, will also take part. He said: "Four years after the start of the conflict, the blood of more than 200,000 murdered Darfuris stains the deserts of Darfur.
"The lives of the local population lie in tatters, as does the reputation of the international community."
On Friday, Tony Blair promised "tougher action" against the Sudanese government and rebels if they failed to act to end the crisis.
The conflict has led to 16 un-enforced UN resolutions and provoked 60 statements of concern from the EU but, according to campaigners, "zero action".
Amnesty International UK Director Kate Allen said: "For four years now, the Sudanese Government has allowed these vicious crimes against humanity to persist... enough is enough."
Millions have been displaced by the conflict
Mr Hain was one of eight Labour politicians involved in the party leadership race to make a statement on the issue.
Left-wing leadership candidate John McDonnell said the failure to take action was "a shameful indictment of a Europe that is more concerned with trade than preventing genocide".
Campaigners said the political statements made for the day of action had to be acted on by whoever was part of the next administration.