RIYADH - Saudi Arabia has launched heavy air strikes on rebels in northern Yemen and is moving troops nearer the border after a raid into its territory by the Shi'ite insurgents, a Saudi government adviser said on Thursday.

Saudi government officials said only that the air force had bombed Yemeni rebels who had seized a border area inside the kingdom, which they said had now been recaptured. The officials said at least 40 rebels had been killed in the fighting.

The Yemeni government -- which has long dismissed accusations by rebels that it has colluded with Saudi Arabia to combat them -- denied that Saudi planes had struck across the border.

Saudi Arabia did not hit targets in Yemen, a Yemeni defense official told Reuters, declining further comment.

Saudi Arabia, the world's biggest oil exporter, has become increasingly anxious about instability and militancy in Yemen, which is also facing separatist sentiment in the south and a growing threat from resurgent al Qaeda fighters.

As of yesterday late afternoon, Saudi air strikes began on their positions in northern Yemen, the adviser said, asking not to be named because operations were still going on.

There have been successive air strikes, very heavy bombardment of their positions, not just on the border, but on their main positions around Saada, he said, alluding to the capital of the northern province where the rebels have been battling Yemen government forces since August.

Al Jazeera television quoted a rebel spokesman as saying the Saudi air force had raided six locations inside Yemen. One position had been hit by about 100 missiles in one hour.

Saudi Arabia said on Wednesday a security officer was killed and 11 were wounded in an attack by gunmen who had crossed the border from Yemen -- the first such reported incursion since the long-running Houthi revolt flared up again in August.

The Saudi-owned Elaph website reported that a second soldier had died later from the same clash.

NO DECISION ON GROUND OPERATION

The Saudi government adviser said no decision had yet been taken to send troops across the border, but made clear Riyadh was no longer prepared to tolerate the Yemeni rebels.

After what happened yesterday, it is clear they have lost track of reality and it has got to a point where there is no other way. They have got to be finished, he said.

An al Qaeda group said on Thursday it was behind an ambush this week in which seven Yemeni security officials were killed.

The Shi'ite rebels, known as Houthis after the family of their leader, have previously accused Saudi Arabia of backing Yemen's armed forces in the conflict. Sanaa had denied this.

The rebels said on Wednesday they had taken control of the Jabal al-Dukhan area after defeating Saudi forces there.

Saudi Arabia was allowing the Yemeni army to use the mountainous area to launch attacks against them and they would take action if this continued, the rebels said.

Al Arabiya television reporter Mohammad al-Hasan, speaking by telephone from Jabal Dukhan, said fighting was in progress.

We hear bullets and artillery from time to time and we see columns of smoke rising...There was intensive bombing by Saudi warplanes yesterday evening and this morning on Jabal Dukhan and some of the surrounding mountains...mainly to the east, Hasan said, adding that the air raids had stopped several hours ago.

A Houthi statement said the raids had caused civilian casualties, but gave no details.

The 1,500 km (930 miles) border between Yemen and Saudi Arabia is a security worry for the kingdom, which is building a high-tech border fence to prevent infiltration.

Saudi Arabia and the United States fear the conflict in Yemen's north and a separatist movement in the south will loosen already tenuous government control and empower al Qaeda.

Such fears rose in August, when a Yemen-based suicide bomber posing as a repentant al Qaeda militant tried to kill Saudi Arabia's counter-terrorism chief, a member of the royal family.

U.S.-allied Arab countries such as mainly Sunni Muslim Saudi Arabia and Egypt fear 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.

Yemen's army launched Operation Scorched Earth in August to crush the rebellion. Aid groups say around 150,000 people have been displaced by the fighting, which first broke out in 2004.

The rebels say they are fighting political, economic and religious marginalization by Yemen's central government.

(Additional reporting by Mohamed Sudam in Sanaa and Alistair Lyon in Beirut; writing by Alistair Lyon)