The kingdom's warships were ordered on Tuesday to search any ship suspected of carrying weapons or fighters near the Yemeni coast, a government adviser said, as Riyadh vowed to continue its offensive against the rebels until they pull back from the border area.
Despite a warning by Iran to keep out of Yemen's affairs, Prince Khaled bin Sultan, the Saudi deputy defence minister, pledged to keep up the military offensive against the Houthi rebels on Tuesday, as he visited Saudi troops in the kingdom's southwest Jizan province.
"We are not going to stop the bombing until the Houthis retreat tens of kilometres inside their border," he said.
His comments came as the rebels announced they had taken control of more territory on the border with Saudi Arabia, heightening concerns about growing instability in the region.
The fighters released a statement on Tuesday, saying: "Full control was taken last night over Qatabar directorate and control of all supplies and ammunition as well as buildings and other military sites."
Yemeni officials could not immediately be reached for comment.
Qatabar lies in the mountainous northern province of Saada, which borders Saudi Arabia, the world's leading oil exporter.The northern province has also been the scene of most of the fighting that has taken place in recent months between Yemeni government forces and the rebels.
Saudi forces have launched a series of military strikes in recent days against the Houthis after the fighters killed a Saudi soldier in a cross-border raid last week.
Riyadh has become increasingly anxious about instability in Yemen, which is facing opposition from the Shia population in the north, separatist sentiment in the south and a growing threat from resurgent al-Qaeda fighters.
The 1,500km border between Yemen and Saudi Arabia is a security worry for the kingdom, which is building a high-tech border fence to prevent infiltration.
Al Jazeera's Hashem Ahelbarra, reporting from the Yemeni capital, Sana'a, said: "We are amid a campaign and a propaganda war with both sides saying they have made huge advances.
"Saudi Arabia is a key player in Yemen, it has loyalty of tribal leaders, politicians and religious leaders here.
"Saudi Arabia prides itself by saying they are the protectors of Sunni Islam and while 80 per cent of Yemen's population is Sunni, they say it is their moral obligation to protect Sunnis everywhere in the world."
Saudi Arabia also has concerns that the Houthis are being used by Iran to fight a proxy war against it.