After several months of relative calm, intense fighting resumed last month around the city of Goma, the capital of North Kivu province.
The DRC, the United Nations and Western countries say Rwanda is supporting the rebels in a bid to control vast mineral resources, an allegation Kigali denies.
The clashes have left at least 35 civilians dead and hundreds wounded, Tigere Chagutah, Amnesty's regional director for east and southern Africa said.
"Thousands of civilians are again being caught between crossfire and are desperate for humanitarian assistance," he added.
More than one million people are now in and around Goma after fleeing the fighting, he said.
Clashes were ongoing on Tuesday near Bweremana, about 15 kilometers (nine miles) west of Goma, according to residents and the local civil society reached by telephone.
The United States-based Center for Civilians in Conflict on Tuesday denounced the use of heavy artillery and mortar shells against civilian installations.
France has called on Rwanda to end "all support" for M23 rebels in DRC and to pull its troops out of the vast neighboring country.
The United States on Saturday also strongly condemned growing violence by the M23, saying the group's backers in Rwanda must remove sophisticated ground-to-air missiles that are threatening lives in the country's east.
Kigali responded a day later that the US statement "fundamentally distorts" the situation, while acknowledging having taken "measures to ensure complete air defence of Rwandan territory."
After years of dormancy, the M23 (March 23 Movement) took up arms again in late 2021 and has since seized vast swathes of North Kivu province.
Since early February, Goma, which stands between Lake Kivu and the Rwandan border, is practically cut off from the country's interior.
The DRC army is supported by myriad local armed groups, two foreign private military companies and the presence of UN peacekeepers and troops from the Southern African Development Community.
Amnesty International Calls for Combattants to End 'Deliberate' Attacks on Civilians
GOMA, DRC -Amnesty International on Tuesday called for an immediate halt to "deliberate and indiscriminate attacks on civilians" in fighting between government forces and M23 rebels in eastern Democratic Republic of Congo.
Forum