Olympics Minister Tessa Jowell has backed using the run-up to the Beijing Games to urge China to do more to improve the situation in Darfur.
The Olympics Minister said a boycott was not necessary
She said it was "reasonable" to put pressure on China to use its influence on the Sudanese government to end the humanitarian crisis.
But Ms Jowell said any boycott of this year's Olympics would be a "great pity" and not "serve any purpose".
An estimated 200,000 have died in fighting in Darfur since 2003.
About 2.5 million people have been displaced.
Pressure on the Chinese authorities to take action has increased this week.
Film director Steven Spielberg resigned as an artistic director of the Beijing Games.
And a group of Nobel Prize-winners and athletes sent a letter to the Chinese president, asking him to use his influence in Sudan to end the conflict in Darfur.
Ms Jowell told BBC Radio 4's The World at One: "I certainly think it's reasonable to use this window to encourage China to act as a responsible global citizen."
But she added: "I think the boundary between government and sport is one that politicians should cross very carefully."
Ms Jowell said China had a "poor, disturbing record on human rights" but said diplomatic efforts were ongoing, often without any publicity.
Freedoms given to journalists during the Games "should not and cannot be taken back", Ms Jowell said.
Earlier, Ms Jowell told The Times newspaper: "The world has known for the last seven years that Beijing would host the Olympics.
'Urgency of Darfur'
"Most progressive governments accept that there are wholly unacceptable aspects of Chinese policy but that did not stop the International Olympics Committee (IOC) awarding them the Games.
"A call for a boycott doesn't serve any purpose and it would be a great pity. This doesn't mean, however, we should we distracted from the urgency of Darfur."
Sudan, with its vast oil reserves, sells some two-thirds of its oil to Beijing.
In turn, Beijing sells weapons to the Sudanese government and has defended Khartoum in the UN Security Council.
As a result, China has been criticised for its links with a government ostracised by many for its role in the ongoing crisis in Darfur.
On Tuesday, as part of a "Global Day of Action" focusing on Darfur, the open letter signed by Nobel Peace Prize laureates and former Olympians was sent to China's president, Hu Jintao.