Russia backed a proposal for an emergency cease-fire in Syria as the military bombed the city of Homs for nearly a third week, killing dozens of people on Wednesday, including two Western journalists, and raising pressure on world powers to agree on measures to halt the deteriorating humanitarian situation.

The U.S. also said it supported the proposal by the International Committee of the Red Cross, which is in talks with Syria's government and members of the opposition on a two-hour daily truce that would allow for the entry...