The ceasefire will not apply to the jihadist groups Islamic State or Jabhat Fateh al-Sham, known as the Nusra Front until it broke formal allegiance to al Qaeda and changed its name.
The rebel groups writing to the United States said the exclusion of Jabhat Fateh al-Sham, which operates only inside Syria, while including Iran-backed foreign Shi'ite militias that operate across international borders showed a double standard.
They added in their letter that its exclusion from the ceasefire would be used by Russia as a pretext to bomb other rebel groups, citing their experience of a failed cessation of hostilities earlier this year.
The Syrian air force bombed Islamic State targets near Palmyra, state television reported on Sunday, while rebels clashed with the group northeast of Damascus, the Syrian Observatory for Human Rights, a U.K.-based war monitor said.
The United States warned insurgents on Saturday they would face "dire consequences" if they cooperated with Jabhet Fateh al-Sham, which fought alongside a range of mainstream and Islamist rebel groups during intense battles in recent weeks in southern Aleppo.
Ahrar al-Sham, one of the largest Islamist groups among the rebels, which has fought alongside Jabhat Fateh al-Sham, criticised the deal in a videotaped speech celebrating Islam's Eid al-Adha festival, which falls on Monday, without rejecting it outright.
It said the deal failed to meet the minimum goals of the movement and would increase the suffering of the Syrian people. It also attacked what it called the "singling out" of particular groups, apparently a reference to the exclusion of Jabhat Fateh al-Sham.
Illustrating how widely insurgents work with the former al Qaeda affiliate, Ahrar al-Sham was one of several rebel groups to announce the launch of an offensive in the southwest in coordination with Jabhat Fateh al-Sham on Saturday.
Insurgents posted footage said to show battles on that front on Sunday which Reuters could not verify.
In Latakia province, violent clashes continued on Sunday two days after the army and its allies launched an offensive around several villages near the main coast road to Aleppo using heavy artillery fire and dozens of air strikes, the Observatory said.
More air strikes were reported in Aleppo and Idlib province on Sunday after scores of people were killed in aerial bombardment on Saturday. One in the town of Saraqeb hit a civil defence centre where civilian rescuers are based, injuring several, according to the Observatory.