Warplanes have carried out more than 30 strikes on the northwestern Yemeni provinces of Saada and Hajja near the border with Saudi Arabia, local officials and residents said.
The air raids occurred after Yemeni rebels fired rockets and mortars into Saudi Arabia on Tuesday, reportedly killing at least three people in the border town of Najran.
Houthi sources told the Reuters news agency that 43 civilians were killed and at least 100 wounded as a result of the air strikes, which lasted until dawn on Wednesday. The figure could not be independently verified.
Local sources also said there was heavy artillery shelling coming from the Saudi border.
OPINION: Humanitarian crisis of immense magnitude looms in Yemen
Saudi authorities said that armed Houthi fighters carried out attacks on Tuesday in the town of Najran, forcing authorities to suspend all flights at a local airport, and shut down all schools.
| Yemen's Foreign Minister Riyadh Yaseen: Bombing necessary despite civilian casualties
The AFP news agency reported that three people were killed in the cross-border mortar bomb and rocket attack, citing Riyadh's interior ministry said.
It did not specify if those killed were civilians or troops.
In a statement, Saudi Brigadier-General Ahmed Asiri said that Saudi-led coalition forces would respond to the Houthi attack.
"What happened today is part of the chaos that the Houthi militias live with," he said, adding that "all options are open" to the kingdom to ensure its security.
The border area has been a flashpoint for Saudi-Houthi clashes amid a Saudi-led coalition's air campaign targeting the rebels in Yemen.
"This is a major development in this war," said Al Jazeera's Mohamed Vall, who is reporting from the Saudi capital Riyadh.
"Up until now we have seen attacks on soldiers near the border, but not in the city [of Najran] itself."
He said the latest attack complicates the work of the Saudi military, who now faces the challenge of securing the border, while carrying out air strikes inside Yemen.
Last Thursday, border clashes left three Saudi troops and dozens of rebels dead.
Relief operations centre
News of the latest violence comes as Saudi King Salman announced at a meeting of Gulf leaders the establishment of a centre to coordinate relief operations for Yemen, and invited the United Nations to join in the effort.
"We hope that the United Nations will participate effectively with what this centre will shoulder, including coordinating all humanitarian and relief works for the Yemeni people with the participation of the countries that are supporting the Gulf initiative," he said in a speech in the Saudi capital.
On Monday, Saudi's foreign minister, Adel-al Jubeir, had said that his country was considering temporary halts in coalition air strikes against the Houthis, to allow for aid deliveries.
For his part, John Kerry, US secretary of state, will visit Riyadh for discussions with Saudi government leaders on May 6 and May 7 to discuss the "humanitarian pause".
The UN has repeatedly warned that impoverished Yemen faces a major humanitarian crisis and calls have been growing for efforts to increase aid deliveries.
The UN has called for a humanitarian pause in the conflict, as relief agencies said they desperately need supplies, including fuel to run infrastructure such as hospitals.
It warned that key infrastructure in the war-torn country, including water supplies, health services and telecommunications, are on the verge of breaking down due to a major fuel shortage.
At least 1,200 people have been killed in fighting in Yemen since March 19 and thousands more have been wounded, according to the UN. It estimates that at least 300,000 people have been displaced by the conflict.
Source: Al Jazeera And Agencies