SANAA, Yemen – Yemen's embattled leader on Monday rejected demands that he step down, saying widespread demonstrations against his regime are unacceptable acts of provocation.

However, U.S.-backed President Ali Abdullah Saleh, in power for three decades, offered to begin a dialogue with the protesters. The proposal was quickly rebuffed as insincere by an opposition spokesman.

In another attempt to defuse anger, Saleh told a news conference that he has ordered troops not to fire at anti-government protesters, except in self defense. At least 11 people have been killed since protests erupted earlier this month, including a youth shot dead Monday, medical officials said.

The demonstrations in Yemen, the poorest Arab nation, are part of a wave of unrest that have swept across the Arab world in recent weeks and toppled autocratic leaders in Tunisia and Egypt.

Saleh's government was already weak before the protests, facing a southern separatist movement and disaffected tribesmen around the country. Saleh is quietly cooperating with the U.S. in efforts to battle an al-Qaida franchise that has taken root in Yemen, but his government exercises limited control in the tribal areas beyond the capital. The U.S. gives Yemen military aid and training.

Despite Saleh's gestures, protesters are digging in. Several hundred camped overnight in a square in the capital of Sanaa, near the city's university. Similar to the scenes in Tahrir Square in Cairo, the epicenter of the Egyptian uprising, protesters in Sanaa pitched small tents and set up a platform equipped with loudspeakers. Protesters guarded access roads and searched those entering the square.

In the city of Taiz, tens of thousands of protesters rallied in the central square. "We will not leave this place until the downfall of the regime," activist Ahmed Ghilan said.

On Monday, a 28-year-old protester died of wounds he sustained when a hand grenade was thrown on protesters in Taiz on Friday, a hospital official said.

In the town of al-Maafer, in Taiz province, witnesses said armed men opened fired Sunday evening and injured three protesters.

In the port city of Aden, a group of youths threw stones at a security vehicle Monday, said a medical official at a local hospital. Shots were fired at the stone-throwers from the vehicle, killing one and injuring four, the official said.

Saleh claimed Monday that government opponents are a small minority and that those who want to see him leave should compete in elections. The next scheduled vote is in 2013.

"The opposition has raised the ceiling of demands calling now for the regime's down fall. This is unacceptable and those who want power should resort to the polling boxes," he said.

He described the demonstrations as an unacceptable provocation, rejecting what he suggested were attempts at foreign interference. "The arbiter is the (Yemeni) people and not the U.S. embassy, the United States or the EU," he said.

Mohammed al-Sabri, a spokesman for a coalition of opposition groups, rejected Saleh's call for dialogue. "The call is merely an attempt to win time and we have been in this vicious circle for years," he said.

The European Union delegation in Yemen urged authorities in a statement to "immediately halt attacks by security forces and armed pro-government groups on peaceful protesters and journalists and avoid any escalation. "