Seven Saudi soldiers have been killed in border attacks by Yemeni "militias," a Saudi-led military coalition that backs the Yemeni government said on Sunday.

The escalation of clashes on the Saudi-Yemeni border came despite ongoing peace talks in Kuwait City between the Saudi-backed Yemeni government and the Houthi rebels and allies, who control the capital Sana'a.

The soldiers were killed fending off a number of cross-border infiltration attempts Saturday by Houthi fighters and supporters of former Yemeni president Ali Abdullah Saleh, the Saudi-led coalition said.

The Houthi movement's al-Masirah television showed footage of rocket attacks on what it said were Saudi positions across the border, and claimed that a Saudi colonel had been killed in one of the attacks.

Al-Masirah said that the Yemeni army and Houthi fighters were carrying out "intensified attacks ... on the front lines on the far side of the border in response to the continued Saudi-American aggression."

The last two weeks have seen the most intense clashes along the border since the two sides agreed on a pacification regime for the area in March.

The announcement of the Saudi losses came hours after the Yemeni government said it had signed off on a peace framework proposed by UN envoy Ismail Ould Sheikh Ahmed at the Kuwait talks.

Ould Sheikh Ahmed did not reveal the details of his plan, but a government statement said it called for the withdrawal of forces from Sana'a and other major cities held by the Houthis to pave the way for a political dialogue process.

The envoy's framework also called for the dissolution of a ruling presidential council established by the Houthis on Thursay, according to the statement.

Houthi negotiator Hamzah al-Houthi expressed disappointment at the proposals, saying his delegation had told the envoy they wanted the talks to bring about a comprehensive agreement covering political as well as security issues.

Yemen's civil war intensified in early 2015 when Houthi and pro-Saleh forces moved on Hadi's temporary capital in the southern city of Aden, prompting Saudi Arabia to launch an air campaign in support of the government.

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