The rebels claim Saudi planes have bombed Yemeni villages
Saudi Arabia has insisted its forces only attacked Yemeni rebel positions on Saudi territory, according to the state news agency.
This directly contradicts a number of separate reports on Thursday that air strikes had taken place on on rebel strongholds in northern Yemen.
The government said it would continue fighting to drive out all the rebels who had infiltrated across the border.
The rebels say that Saudi airplanes are bombing northern Yemeni villages.
A spokesman for the rebels, who are known as Houthis, alleged on Thursday that a Saudi air strike hit a market in Saada in north Yemen, killing a group of civilians.
The Saudi government has said that its conflict with the rebels began when a Saudi border official was killed and rebels later captured an area of mountainous territory in the Saudi province of Jizan.
The rebels had claimed there were minor clashes with Saudi forces along the border before then.
The Houthis have been engaged in an intense wave of fighting with the Yemeni army since the government launched a major new offensive in August 2009.
They have long alleged that Saudi Arabia has been giving support to the Yemeni regime, a claim both governments denied, but in recent weeks Saudi forces have been overtly drawn into the fighting.
The Houthis, named after the family of their leader, say they want greater autonomy and a greater role for their version of Shia Islam. They complain that their community is discriminated against.
The Yemeni government accuses the rebels of wanting to re-establish Zaidi Shia clerical rule, and of receiving support from Iran.
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.
Aid agencies say tens of thousands of people have been displaced in the latest round of fighting.