The new president of the opposition Syrian National Coalition has described the rebels' military position as weak - but vowed the situation would improve with weapons shipments from Saudi Arabia arriving soon.
In an interview on Sunday, Ahmad Jarba told the Reuters news agency that the opposition would not consider attending a proposed US and Russian-sponsored peace conference in Geneva until its position strengthens.
"Geneva in these circumstances is not possible. If we are going to go to Geneva we have to be strong on the ground, unlike the situation now, which is weak," he said. "We cannot go to Geneva unless we are strong."
Jarba, who was elected on Saturday, said he expected advaced weapons from his backer Saudi Arabia would arrive on the front lines soon, and help tip the scales in the rebels' favour.
"I think the situation is better than before. I think these weapons will arrive to Syria soon," he said.
"I will not rest until I procure the advanced weapons needed to hit back at Assad and his allies. ... I give myself one month to achieve what I am intent to do," he added.
After meeting a delegation from Homs, Jabra donated $250,000 of his own money to support humanitarian relief efforts in the city. Activists who met Jarba said the remaining rebellious Sunni neighbourhoods in Homs could fall in days.
Jarba offered Assad's forces a truce for the duration of the holy month of Ramadan to stop fighting in the besieged city of Homs, where rebels face a ferocious ground and air onslaught by regime forces and fighters from the Lebanese Shia group Hezbollah.
"We are staring at a real humanitarian disaster in Homs. Assad, whose military machine was on the verge of defeat, became propped up by Iran and its Hezbollah proxy," Jarba said.
Fighting in the city continued on Sunday, according to activists.
Amateur video footage, which cannot be independently verified, showed shelling near the Khalid ibn al-Walid mosque.
Government forces are said to have been using heavy air raids and artillery strikes in Homs to gain ground.
Opposition forces have retained control in much of the north and east of Aleppo province despite regime attacks.
Six prisoners were reported killed in an artillery strike on the central prison in Aleppo, said the British-based Syrian Observatory for Human Rights, which communicates with a network of activists on the ground.
The explosives hit on Friday night, the Observatory said, but added that it was not clear who fired the shells.
The Observatory reported about 70 soldiers and fighters were killed on Sunday, as well as 40 civilians, in clashes across Syria.