Saudi F-15 and Tornado jets targeted strongholds of the Houthi rebels on the Yemeni side of border, spokesmen for the group and Arab media said.
But officials in Sanaa denied there had been any attacks on Yemeni territory.
The attacks came after a Saudi officer was killed and 11 were wounded in a raid by the rebels on the Jizan region.
The Houthis said on Wednesday that they had taken "full control" of a mountainous section of the border region of Jabal al-Dukhan.
In a statement on its website on Wednesday, the group said Saudi warplanes and helicopters had dropped phosphorus bombs on its fighters in the areas of al-Malahaid, Jabal al-Mamdud, al-Husama and al-Mujdaa.
On Thursday, a rebel spokesman based in Europe, Yehya Badr al-Din al-Houthi, told the BBC Arabic service that the attacks had continued.
"Yesterday, the Saudi aircraft attacked villages in the Ghamr district. They destroyed homes and killed and wounded 10 people, mainly women and children," he said.
"Today, the Saudi aircraft continued striking the village of Hasama and other villages near the Malaheez area."
Another spokesman for the group said civilians had been killed when bombs were dropped on a local market in Saada province, and that one rebel location had been hit by about 100 missiles in one hour.
A Saudi government adviser said the air force had targeted rebels who had seized Saudi parts of Jabal al-Dukhan, which they said had now been recaptured by troops.
The official said at least 40 rebels had been killed in the fighting.
"As of yesterday late afternoon, Saudi air strikes began on their positions in northern Yemen," the unnamed adviser told Reuters.
"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 added.
A Yemeni defence ministry spokesman would only deny "the rebels' allegations of Saudi air raids against Yemeni villages", the AFP news agency said.
The London-based Arabic newspaper Elaph meanwhile reported that Saudi ground forces were also moving towards the Yemeni border.
The deployment was later confirmed by Arab diplomats, who told the Associated Press that army units and special forces were amassing in the area, and that several nearby Saudi towns and villages had been evacuated.
Saudi reconnaissance teams believed there were between 4,000 and 5,000 Houthis based in the mountainous border region, Elaph said.
The Saudi government adviser said no decision had yet been taken to send troops across the border, but made it clear that Riyadh was no longer prepared to tolerate the Yemeni rebels, Reuters reported.
"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.
The Yemeni government accuses the rebels of wanting to re-establish Zaydi Shia clerical rule, and of receiving support from Iran.
Earlier in the week, 10 rebels captured in 2008 were sentenced to death.
The Zaidi Shia community are a minority in Yemen, but make up the majority in the north of the country.
The insurgents first took up arms against the government in 2004, after which government forces killed or captured much of the Houthi leadership.
The government launched a fresh offensive in August 2009 which has precipitated a new wave of intense fighting.
Aid agencies say tens of thousands of people have been displaced.