As many as 3,000 British troops will be sent as part of the 10,000- or 12,000-strong force, which would include elements from the United States, Canada, France and South Africa, among other nations.
Speaking in Downing Street, Mr Rifkind said: "Such is the humanitarian crisis facing the people, the UK is prepared to play its part, including a military contribution."
Today, Mr Rifkind flies to Paris for urgent discussions with France, the US and Canada. Although the exact size and shape of the force still has to be determined, the idea is to stabilise the situation and hand over to African forces after three months.
The decision to commit troops follows a meeting of the Cabinet's Overseas Policy and Defence Committee yesterday afternoon, where Field Marshal Sir Peter Inge, the Chief of Defence Staff, briefed the committee.
Sources stressed that a force of this size would mostly comprise logistical support troops, engineers and medical staff - needed to help deal with up to 1 million refugees - and not combat infantry. However, there is a strong feeling that if Britain does commit a force, it has to be big enough to look after itself, even as part of a multinational - and primarily Nato - contingent.
Units from Britain's Joint Rapid Deployment Force (JRDF), comprising 5th Airborne Brigade, based in Aldershot and 3rd Commando Brigade, based in Plymouth, are always on standby to move to trouble spots quickly.
The US also confirmed that it would send soldiers. The White House announced that it would send US troops "in limited fashion", including 1,000 to secure an airport at Goma in eastern Zaire, and several more thousands to the region to provide logistical support. The US is expected to play a leading role in providing transport and communications. US troops were already in Uganda yesterday, to inspect airports and other facilities.
The multinational force being assembled would aim to secure an aid corridor from Kigali in Rwanda to Goma. But its precise mission and make-up will be defined over the next few days, at the meeting in Paris and at the United Nations in New York, where diplomats were preparing last night for a session of the Security Council.
On Tuesday, the UN Secretary General Boutros Boutros-Ghali confirmed reports that Canada had offered to lead a multinational military force into eastern Zaire. He said he expected more than 12 countries to make up the Canadian-led force and hoped that the US would provide air transport and supplies.
In Paris, French officers said the first, 600-strong French detachment, which could leave within 24 hours, was from the 8th Marine Infantry Parachute Regiment, based at Castres in south-west France. The regiment has recently served in Africa and Bosnia. A second battalion, from the 3rd Marine Parachute regiment, could leave within another 24 hours.
But the French presence is controversial in the region, where France is regarded as far from neutral. It is suspected of having helped to supply aid to Hutu rebels in Rwanda.
France's neutrality is also compromised by the presence in his villa on the Riviera of the Zairean leader, President Sese Seko Mobutu. The rebels in Zaire want to remove Mr Mobutu.
Rwanda has said outright that French troops should not take part in any force that might be agreed, while Tutsi leaders in eastern Zaire were quoted as threatening to attack any French troops taking part in a multinational force.
French forces have already begun aerial reconnaissance of eastern Zaire. The French defence ministry said that it wanted to assess the feasibility of landing and protecting large consignments of aid. It said that existing airports on the Zaire-Rwanda border were regarded as too small and too unsafe, and that airports in Uganda and the Central African Republic were being considered. But yesterday, Zairean rebel troops in Goma fired on an aircraft which they believed to be French, raising fears that an intervention force will meet a hostile welcome.
US bows to pressure, page 10
A long tradition
n The mission in Zaire will be the largest British deployment to sub-Saharan Africa since the anti-colonial conflicts of the Fifties and Sixties. It is part of a long tradition of - sometimes unsuccessful - British intervention.
n In 1879, during the Zulu War, 1,500 British troops were massacred at Isandh- lwana, but many VCs were won at Rorke's Drift.
n In the 1880s, the British tried to suppress an uprising in Sudan but in 1885, General Gordon was besieged in Khartoum and killed.
n From 1899 to 1902, Britain fought the Boer Republic of South Africa, and won only after committing a quarter of a million troops.
n In the 1950s, Britain committed up to 14,000 troops to suppressing the Kenyan revolt.
n British troops helped to supervise the transition from Rhodesia to Zimbabwe, and in 1994, British troops were part of the UN force put into Rwanda.Reuse content