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Explosions and heavy gunfire was heard in the Shida and al-Hisama districts of Saada province and near the town of Haradh in neighboring Hajja province.
Saudi helicopters were flying overhead, residents said. They described the fighting as the worst in the area during six days of Saudi-led air strikes against Houthi targets throughout Yemen, which are aimed at weakening the Iran-allied militia.
"The bombing today is worse than on any other day and we hear sounds of explosions and see Saudi planes in the air," Khaled, a resident in the Haradh area told Reuters.
The Houthi TV channel al-Maseerah also reported clashes on the frontier. "Rockets from the Saudi-American aggression continue to fall on the Shida and al-Hisama districts on the Yemen-Saudi border," it said in a text message.
Tension in the border area has mounted since an air strike killed at least 40 people at the Mazraq camp for displaced people near Haradh on Monday. A humanitarian official said the strike targeted a truck full of Houthi gunmen.
An air strike that killed at least 40 people at a camp for displaced people in north Yemen was a violation of international law and those responsible should be held accountable, the United Nations said on Tuesday.
Some 200 people were wounded, dozens of them seriously, the International Organization for Migration said. "We have not identified who is responsible for this attack," UN spokesman Farhan Haq said. "Whichever forces are hitting them are in violation of the law, there should be accountability for that and ultimately all such attacks have to cease."
Saada and neighbouring northern provinces are strongholds of the Houthi movement, a militia belonging to Yemen's Zaydi Shiite sect, which fought a brief and indecisive ground conflict with Saudi Arabia in 2009.
Meanwhile,The United Nations said Tuesday that the last of its international staffers have now left Yemen as the UN human rights chief warned of a "total collapse" in the Arab world's poorest country.
The deputy spokesman for the UN secretary-general, Farhan Haq, said the remaining 13 international staffers were out as of Tuesday and that the UN would do what it can with the hundreds of local staffers who were still there. The UN human rights office in Geneva said at least 93 civilians have been killed and 364 wounded in five Yemeni cities in the past five days as Saudi-led airstrikes pound advancing Shiite rebels. The overall figures are likely much higher. UN officials are calling on all sides to protect civilians from harm in the fighting.
Houthi militiamen and allied army units shelled Aden overnight Monday while Saudi-led coalition jets bombed their positions near the airport, killing at least 36 people, officials and witnesses said.
Iran-allied Houthis are pushing on the outskirts of the city, the last bastion of Yemeni President Abd-Rabbu Mansour Hadi, despite six days of Saudi-led air strikes meant to stem their advance.
Artillery fire on the Khor Maksar district of Aden killed 26 people overnight Monday, a health ministry official said.
Shells hit a residential building in the area close to a private residence once used by Hadi -- who is now abroad in Saudi Arabia -- killing ten militiamen loyal to the president, a witness told Reuters.
Coalition planes bombed Houthi fighters and their army allies in the area of the airport, which has traded hands between the two warring sides during over a week of heavy fighting. It was not immediately clear if there were any casualties.
Residents of the city reported shops were shuttered and streets were deserted for fear of worsening security.
In the southern province of Dhalea, Hadi loyalists, who were backed up by five coalition air strikes on Tuesday, reported heavy shelling and street fighting with the Houthis and their allies.