Baghdad, Iraq ? The Iraqi prime minister insisted Sunday that the raging insurgency, which has claimed 300 lives in the last week alone and resulted in a wave of kidnappings, will not delay January elections, promising the vote would strike a “major blow” against the violent opposition.

Meanwhile, a grisly videotape posted on a Web site showed the beheading of three hostages believed to be Iraqi Kurds accused by militants of cooperating with U.S. forces. A separate group also claimed to have captured 18 Iraqi soldiers and threatened to kill them unless a detained aide of radical Shiite cleric Muqtada al-Sadr was freed, according to the Arab news station Al-Jazeera.

In another sign of continuing instability 17 months into the U.S.-led occupation of Iraq, a suicide car bomb killed three people in Samarra — a northern city that U.S. and Iraqi commanders have portrayed as a success story in their attempts to put down the insurgency.

Over the past week, about 300 people have been killed in escalating violence, including bombings, street fighting and U.S. airstrikes. Last week, U.N. Secretary-General Kofi Annan warned there could not be “credible elections if the security conditions continue as they are now.”

But Iraqi Prime Minister Ayad Allawi, who is heading to the United Nations for this week’s General Assembly session in New York, said his interim government was determined “to stick to the timetable of the elections,” which are due by Jan. 31.

“January next, I think, is going to be a major blow to terrorists and insurgents,” said Allawi, who spoke with reporters after a meeting with British leader Tony Blair in London. “We are adamant that democracy is going to prevail, is going to win in Iraq.”

Allawi, a Shiite Muslim, has been insistent about having elections on time because of pressure from Iraq’s Shiite community and its most powerful cleric, Grand Ayatollah Ali al-Sistani, who fought for early elections. Reneging on the vote would risk angering the generally cooperative Shiite religious establishment.

Rashad Rashid, left, cries while touching the remains of the truck his brother Ziad Rashid was killed in after an improvised explosive device went off under it, in Baghdad, Iraq. Two people were injured in the explosion Sunday.

Shiites, who are in the majority in Iraq, are eager to translate their numbers into political power.

But several cities in the Sunni Muslim heartland north and west of Baghdad are out of U.S. and Iraqi government control, with insurgents holding sway, particularly in the city of Fallujah. That raises questions on whether balloting can be held there — and the legitimacy of elections held without adequate Sunni participation.