Ban Ki-moon, the UN secretary-general, and the UN Security Council, have both condemned the attacks by the rebels.
The council warned on Monday that it would take measures against threats to regional stability.
"The Security Council condemns in the strongest terms the attacks conducted by Chadian armed groups since 11 June 2008," the council said.
Am Dam is located 110km from Goz Beida to the northwest, which the rebels briefly occupied on Saturday.
It lies much further from Chad's eastern border with Sudan, and closer to the capital.
"Our objective is not to take towns but to clear obstacles on the road to Ndjamena," Gueddei said.
He also said that their force was strong enough to take the capital.
A rebel alliance is said to be making its way towards Ndjamena to depose Idriss Deby, the Chadian president.
They last attacked the capital in February and made an attempted coup in 2006.
EU troops attacked
European Union peacekeepers (Eufor) have said that they were attacked near Goz Beida on Saturday, forcing them to return fire.
The troops are deployed to the area to protect refugees, civilians and aid workers in eastern Chad.
There are around 500 Irish and 70 Dutch troops from the Eufor contingent in the region, whose mission is to protect civilians and refugees fleeing the violence in Darfur region of Sudan, just over the border.
The European Union is deploying a total of 3,700 troops, including 2,200 French soldiers, to help protect Sudanese refugees and Chadians uprooted by the conflict.
Eastern Chad is a temporary home to some 300,000 refugees who have fled the Darfur conflict in Sudan.
The region also has camps for 187,000 Chadians displaced by fighting both locally and in Darfur.
Source: Al Jazeera and agencies