By Cynthia Johnston

DUBAI (Reuters) - Yemen's Shi'ite rebels are ready for talks with the government once fighting stops, their leader said on Saturday, responding to a presidential plea as fears grow that al Qaeda could exploit the country's instability.

Abdul-Malik al-Houthi, leader of the northern Yemen-based rebels, also denied that his group was targeting neighboring Saudi Arabia which has been drawn into the conflict.

He was responding to a New Year's plea by President Ali Abdullah Saleh offering to extend a hand of peace if insurgents fulfilled conditions including abandoning violence, releasing prisoners and agreeing to stop attacks on Saudi territory.

"We welcome the call by the president of the republic to return to dialogue, and consider it a positive call and a right step to peace and a return to security and stability," Houthi said in a statement.

"We confront aggression and defend ourselves, and when the war stops, we are ready for dialogue," he said in the statement, carried on a rebel website.

There was no immediate response from the Yemeni government.

The United States and Saudi Arabia fear al Qaeda could exploit instability in Yemen, which also faces separatist sentiment in the south, to turn the Arab country into a launchpad for more international attacks.

Al Qaeda's regional wing said it was behind a Christmas Day attempt to blow up a U.S. passenger jet. The Nigerian who tried to set off the bomb said he had received training and equipment in Yemen.

The Shi'ite rebels from the Zaidi sect have been fighting government troops in Yemen's mountainous north since 2004, complaining of social, economic and religious marginalization.

The conflict, which has killed hundreds and displaced tens of thousands, drew in Saudi Arabia in November when the rebels staged a cross-border incursion into the world's biggest oil exporter.

The Yemeni president, writing in the state's al-Thawra newspaper, had called on the northern rebels and southern separatists on Friday to abandon violence and urged anyone tempted by al Qaeda to reconsider.

"The time has come to lay down your weapons, to steer clear of the violence and the terror and evil acts so as to save your souls and be good citizens in your society," Saleh said.

The minority Shi'ite rebels have already said they were ready for talks to end fighting with Saudi Arabia. Houthi said his group was not looking for a fight with its mainly Sunni Muslim neighbor.

"With respect to Saudi land, we have stressed since the beginning of the Saudi aggression on Yemeni land that we do not target Saudi territory. But we faced a direct aggression from its territory," he said.

U.S.-allied Arab countries such as Saudi Arabia and Egypt are concerned that Shi'ite power Iran could gain influence in Yemen through the Houthis. The rebels deny getting any help from Tehran, which has offered to mediate in the conflict.

(Additional reporting by Tamara Walid in Dubai and Mohamed Sudan in Sanaa; editing by David Stamp)