Saudi Arabia said on Tuesday the conflict was nearing an end, with at least 73 of its troops killed in fighting against Yemeni rebels since November.
Yemeni rebels, however, said the war was far from over.
King Abdullah told al-Seyassah that his orders to the army were to "only drive away infiltrators and preserve the security and borders" of the kingdom.
"We are not a nation that interferes in other countries' affairs and do not accept other countries to interfere in ours," he said.
In November, Saudi Arabia launched a military offensive against Yemen's Shi'ite rebels, known as Houthis after their leader's clan name, after a rebel cross-border incursion.
Saudi Arabia and its ally the United States worry that al Qaeda is trying to use Yemen, where the Houthis are fighting government forces, as a launch pad for attacks in the kingdom and beyond.
The Houthis belong to the minority Zaidi sect of Shi'ism, and complain of social, economic and religious marginalisation, but both rebels and the Yemeni government deny their aims are sectarian.
Houthi leader Abdul-Malik al-Houthi called Saudi Arabia's offensive against the group "unjustified and unnecessary" and accused it of mainly targeting civilians through air raids.
"(Saudi Arabia) targeted areas far from their borders, some further than 100 kilometres away," Houthi told Reuters in an interview.
Houthi denied charges that infiltrators entered Saudi territories, saying they were baseless.
"We have emphasised time and again that we do not target Saudi-controlled areas, as long as they haven't been used against us," he said. Houthi added that Saudi authorities had made a huge mistake by allowing the Yemeni military to use its grounds for launching attacks on rebels.
In southern Yemen, where separatist sentiment has been on the rise, demonstrators marched in several towns to demand the release of those arrested in earlier protests, residents said.
Southern activists have long complained that the government and northerners exploit and discriminate against the south, which holds most of Yemen's oil facilities.
(Reporting by Tamara Walid in Dubai; Mohamad Al-Ghobari in Sanaa; Editing by Richard Williams)
- Reuters - Thomson Reuters Foundation
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