Khaled Abdullah Ali Al Mahdi/REUTERS
Riyadh convened a meeting of Gulf countries on Wednesday to threaten unspecified measures to "protect their interests" in Yemen where the Shi'ite Muslim rebels, allies of its enemy Iran, are holding the president a virtual prisoner.
But unlike in the past, the kingdom wields little influence across its border and has few established ties to Yemen's new power brokers. It has already suspended aid payments, its most potent leverage in the country.
That will compel the Houthis, and by extension Iran, to foot the substantial bill for keeping Yemen afloat if they want to govern the poorest Arab country without Riyadh's support.
Saudi analysts say the priority is sealing the mountainous Yemeni border - where Houthis killed around 200 Saudi soldiers in a brief war four years ago - with a fence modeled on its expensive frontier defenses with Iraq.
"The Saudi strategy is no strategy for Yemen. I don't see one except for security: keeping the border intact and guarding it well," said Jamal Khashoggi, who runs a Saudi news channel owned by a prince.
The Houthi ascendancy means that both the Sunni Muslim kingdom's most populous neighbors, Yemen and Iraq, are now dominated by its biggest regional rival, Shi'ite Tehran.
But Riyadh also worries that the revolutionary Zaydi Shia component of Houthi ideology will raise sectarian tensions. These could drive Yemen's majority Sunnis toward the arms of al Qaeda, which carried out an insurgency inside Saudi Arabia in 2003-06 and wants to unseat the ruling Al Saud family.
Houthi aid dilemma
Khaled Abdullah/Reuters
In Tehran - where politicians have boasted that another Arab capital has fallen to their influence after Baghdad, Beirut and Damascus - Iranian leaders must decide whether to start making its own aid payments to help keep Yemen's economy afloat.
Plunging crude oil prices and the effect of years of sanctions mean Iran has little extra cash to subsidize a country that has historically had a marginal place in the region-wide power tussle between Riyadh and Tehran.
But Ali Larijani, the speaker of Iran's parliament, suggested on Thursday that aid might be forthcoming. "If the people of Yemen would need support, we would of course support them," he told reporters on a visit to Turkey.
So far the Houthis have tried to play a double game, holding the political reins while leaving in charge a president who can take the blame for Yemen's economic problems.
The Houthis welcomed on Thursday proposed concessions by the government on power-sharing but their gunmen still held positions outside the residence of President Abd-Rabbu Mansour Hadi, who remains a virtual prisoner there.
Unless they are prepared to surrender some of the power their fighters have won, the Houthis will eventually have to take responsibility for governing Yemen - and that means they will need money.
The Houthis have their own reasons to distrust Riyadh. The group was founded partly to counter the spread of Saudi Arabia's hardline Salafi form of Islam in Zaydi areas and the kingdom's historical patronage networks among Sunni leaders in the country. For its part, Saudi Arabia added the group to its list of banned "terrorist" organizations in March.
However, Riyadh understands that Houthi ideology and strategy remain relatively fluid and that its leader Abdel-Malek al-Houthi might eventually be swayed by the practical advantages of Saudi assistance to reconsider his group's stance.
Great Wall of Yemen
Khaled Abdullah/Reuters
A report in the Saudi daily al-Yaum on Thursday said Saudi Arabia was working "day and night" to finish its border fence, but the Interior Ministry says it will still take some years to complete.
From the high mountain guard posts on the border, it is easy to see why the work will take time. Ridge after ridge chase each other into the haze, interspersed with deep valleys and dotted with Yemeni villages.
In the lush wadis below, the thick vegetation makes it hard to spot infiltrators crossing the 1,700-km (1,060-mile) border.
The bulldozers of Saudi Binladen Group, the huge Saudi contracting company founded by a Yemeni immigrant whose son created al Qaeda, are crawling over this landscape, building a new road for frontier guards to help keep out militants.
"The old technique of buying off the border tribes no longer works because Iran is paying the Houthis. All we can do is make our defenses stronger," a Saudi guard told Reuters on a recent visit to the frontier.
(Additional reporting By Parisa Hafezi in Ankara and Humeyra Pamuk in Istanbul, Editing by William Maclean and David Stamp)