The army have been fighting northern rebels since 2004
Rebels in northern Yemen say they have clashed with Saudi forces at the site of building work for a fence along the border between the two countries.
A statement on the rebels' website said there were a number of deaths and injuries on both sides.
There was no immediate response from Saudi authorities.
The rebels, known as Houthis, say they are fighting discrimination in Yemen and accuse Saudi Arabia of supporting the Yemeni government.
The group accused Saudi forces of firing on them in the same area on Monday in support of a Yemeni government offensive.
A Yemeni government official told AP news agency that the claim of Saudi involvement in the ongoing conflict was a lie.
The rebels condemned the building of the barrier on the Saudi border: "Residents of the area reject any fence which would have a negative economic impact on them and cut them off from their brethren on the other side," the statement said.
Yemeni officials accuse the rebels in the north of the country of wanting to re-establish Shia clerical rule, and of receiving support from Iran.
Houthi rebels say they want greater autonomy and a greater role for their version of Shia Islam. They complain that their community is discriminated against.
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.
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.