The United Nations Security Council has called on all member-states to back the Chadian government following two days of clashes with rebels in the capital.
The rebels reached the presidential palace at the weekend
France, which has 1,400 troops in Chad, said it hoped it would not have to use the mandate and intervene further.
The French foreign minister said the government of Chadian President Idriss Deby was in control of the capital N'Djamena "for the time being".
Earlier, thousands of people fled the city during a lull in fighting.
Many crossed the river border with Cameroon via the Ngueli bridge or by using boats.
Local officials told the UN refugee agency that thousands were also crossing at the border town of Kousseri and that more were expected.
Aid workers have reported hundreds of injuries to civilians resulting from the intense battles near the presidential palace, with bodies lying in the streets.
After late-night negotiations, UN diplomats agreed a statement condemning the attacks by the rebels, who want to overthrow President Deby, and demanding an end to the violence.
The non-binding statement also gave the green light for countries to "provide support, in conformity with the United Nations Charter, as requested by the government of Chad".
June 2005 - Constitutional changes approved allowing president to stand for third term
April 2006 - Hundreds killed as rebels fight government troops on outskirts of Ndjamena
May 2006 - President Deby wins election boycotted by opposition
January 2008 - EU approves peacekeeping force to protect Darfur refugees from violence in Chad
Chad's permanent representative to the UN wrote to the Security Council on Sunday, appealing for countries to "to provide all aid and assistance needed to help it".
Following the meeting, the US permanent representative, Zalmay Khalilzad, said the French had "the expertise and lead on this issue, and should they decide to do more, they have the support of the Security Council".
BBC world affairs correspondent Mark Doyle says the UN statement presents the French with political and strategic problems.
The French army enjoys its historic military influence in Africa and quietly backs President Deby with weapons and military intelligence, our correspondent says.
But, at the same time, France wants to pursue a modern, European destiny - it wants a French-dominated European Union peacekeeping force, including Irish and Polish troops, to intervene in the crisis, he adds.
The rebels have previously threatened to attack the force because of France's support for the Chadian government, forcing its deployment to be delayed.
French Foreign Minister Bernard Kouchner said he "hoped" his country's armed forces would "not have to intervene further" to support President Deby.
"We do not intend to put French troops more on alert than they are, or to start military operations," he said.
Mr Kouchner said that most of N'Djamena was in the government's hands, but cautioned that the rebels were still operating on its outskirts.
'Window on genocide'
Earlier, the commander the Chadian government forces, Gen Mahamat Ali Abdallah, said the rebels had been "completely routed" in the capital.
However, a rebel spokesman, Abderaman Koulamallah, rejected the claim.
"We have pulled out of the city and we are waiting for the civilian population to be evacuated," he told AFP news agency.
"We certainly will go back on the offensive."
The army has also said it had thwarted a second rebel attack on Adre, near the border with Sudan over the weekend.
The town is where some 240,000 refugees from Darfur are based, living in camps and where the EU force is due to deploy.
The 3,700-strong EU force is intended to protect refugees from the Darfur region of neighbouring Sudan, as well as aid workers.
THE REBEL COALITION
Unified Military Command includes:
Union of Forces for Democracy (UFDD) led by Mahamat Nouri
Rally of Forces for Change (RFC) led by Timane Erdimi
UFDD-Fundamental led by Abdelwahid Aboud Mackaye
Chad has accused the Sudanese government of backing the rebel offensive in Chad in order to stop the EU force from being sent to the region.
Sudan denies this, as well as accusations that it has supported Arab militias accused of ethnic cleansing and genocide in Darfur.
The recent violence began on Saturday, when the rebels seized control of large parts of the capital, approaching the palace where President Deby was holding out.
Mr Deby seized power in a coup in 1990, but has won three elections since then, although their legitimacy has been challenged.