A second night on Wednesday of raids aimed at suppressing further Houthi shelling struck the group's stronghold of Saada, near Yemen's Saudi border, and the small port of Maidi.
"It is possible to repeat the same number of sorties, a land operation is possible, all options are open to prevent these practices of the militias," military spokesman Brigadier General Ahmed Asseri told TV channel al-Arabiya late on Wednesday.
On Thursday, US Secretary of State John Kerry began negotiations in Riyadh to pause the campaign of air strikes launched by a Saudi-led coalition on March 26 to allow aid for Yemenis desperate for food, water and medicine.
In the interview, Asseri did not say whether Saudi Arabia would consider the Yemeni government's request for international troops to relieve the southern city of Aden, where the Houthis took the vital Tawahi district in heavy fighting on Wednesday.
On Thursday, the Houthi-linked Al-Masirah television channel showed the group's fighters in the district and reported that Aden's presidential palace was in their hands.
In a letter addressed to United Nations, the Houthis also called for international action to stop what they described as Saudi aggression and crimes against the Yemeni people.
Earlier, the group said it had shelled a Saudi air defence facility north of Najran after sending mortars and rockets into the city on Tuesday and Wednesday, killing eight people. Another two Saudis were killed by Houthi shells hitting a village in Jizan province.
The Arab coalition has been wary of putting boots onto the ground in Yemen, keenly aware of the difficulties of tackling a well entrenched guerrilla army in its own mountainous terrain.
More than 100 Saudi soldiers were killed during a 2009-10 border war between the kingdom and the Houthis, which included ground fighting in frontier villages. In this conflict 10 Saudi army and border guards troops have died in mortar strikes.
A Saudi Apache was damaged in an emergency landing near the border on Thursday, a Gulf official said. He added that the pilots were safe and denied an earlier report by al-Masirah that the aircraft had been shot down by the Houthis.
Since the coalition started its campaign to push back the Houthis and restore the government of Abd-Rabbu Mansour Hadi, who fled Yemen in March, Asseri has consistently declined either to rule out land operations or say they will occur.
John Kerry’s Meeting
Kerry's first meeting on Thursday was with Hadi, who greeted him warmly, saying: "Good to see you here in Riyadh. Hopefully we will see you in Sanaa soon."
Kerry responded: "There's some work to do."
Later, he will meet Saudi King Salman, who inherited the throne from his brother in January.
The fighting across Yemen killed 120 people on Wednesday, mostly civilians, including at least 40 who were trying to flee the southern port city of Aden in a boat that was struck by Houthi shells, rescue workers and witnesses said.
Kerry has called on both sides to respect humanitarian laws and ensure that civilians are not put in harm's way, suggesting at a Wednesday news conference that he had spoken to his Iranian counterpart to convince the Houthis to agree on a short truce.
Tehran has regularly condemned the Saudi-led air campaign in Yemen although Iran denies accusations from Western and Arab states that it is arming the Shiite Muslim Houthi rebels.
Saudi Arabia, which sees itself as the guardian of Sunni Islam, has long vied for influence with Shiite power Iran.
During his visit, Kerry will also discuss a May 13 summit in Washington with oil-rich Gulf states and talks on curbing Iran's nuclear programme, a senior State Department official said.
The summit will discuss a region-wide defence system to guard against Iranian missiles, which would allay anxieties over any nuclear deal with Tehran, according to U.S. officials. They said the offer could be accompanied by enhanced security commitments, new arms sales and more joint military exercises.
The Houthis and local residents have said Saudi bombardment of northern Yemeni areas since Houthi shelling of the kingdom began on Tuesday has added to civilian suffering in the area.
Villagers from border areas in Hajah province said many had left their homes because of the clashes and were now seeking refuge in other areas where they lacked food.
Most of those displaced were from the Haradh district where there is an important border crossing with Saudi Arabia and which has come under heavy artillery and air attack since the Houthis launched shells from the area at Saudi villages.