'Very much alone'
Catherine Shakdam from the Next Century Foundation told Al Jazeera there was no reason to doubt what the Houthis are saying.
"The video and images coming through are actually affirming the statement. It's a pivotal point in this war that now Yemeni are moving on Saudi land. It's quite interesting to see with all the talk of a grand Saudi coalition that Saudi is very much alone in this fight," Shakdam said.
Yemeni government troops, supported by air strikes of the Saudi-led coalition, have in recent months fought Houthi forces in the Kataf region of Yemen's northern Saada province near the Saudi border. Local sources have said the Houthis have captured scores of Yemeni troops in the battles.
The Saudi-led coalition, which receives arms and intelligence from Western countries, intervened in Yemen in March 2015 after the Houthis ousted the internationally recognised government from power in the capital Sanaa a year earlier.
'War of attrition'
Shakdam said it appears the Houthis now have the upper hand in the conflict as Yemen's people have "rallied around" the rebels because of Saudi human rights abuses, famine, and the immense hardship caused by the war. "This war of attrition has worked against Saudi Arabia... Through their military advances they're gaining access to more weapons, more territory and essentially pushing the Saudi against the wall," she said.
Shireen al-Adeimi from Michigan State University said the attack may change the Saudi leadership's perceptions of the four-and-a-half-year conflict.
"It's incredibly embarrassing for the Saudis giving how much support they have from not only the UAE but also the United States, the UK and several other countries . If the Houthis are able to carry out this level of operation it poses a significant turn in this war," al-Adeimi told Al Jazeera.
The Houthis, who had recently stepped up missile and drone attacks on Saudi cities, have claimed responsibility for the
largest-ever attack on Saudi oil facilities on September 14.
Riyadh dismissed the claim, saying the assault did not come from Yemen and has blamed Iran. Tehran denied this.
The Houthis said on September 20 they would halt missile and drone attacks on Saudi Arabia if the alliance stopped its operations. The coalition has not responded to the proposal.