Saudi Arabia says its troops are ready to defend the border areas
Iranian Foreign Minister Manouchehr Mottaki has warned against foreign intervention in the conflict between the Yemeni government and rebels.
Unidentified parties were adding fuel to the crisis, and attempts to help or to take military action would have negative consequences, Mr Mottaki said.
Correspondents say his comments appear to have been intended for Saudi Arabia.
Shortly afterwards, Riyadh promised it would continue air strikes until the rebels moved back from its border.
"We are not going to stop the bombing until [they] retreat tens of kilometres inside [the Yemeni] border," Deputy Defence Minister Prince Khaled Bin Sultan said, according to the AFP news agency.
Saudi forces launched a ground and air offensive on the rebels, known as the Houthis, after a security officer was killed in a cross-border raid by the group in its south-western Jizan region.
The Houthis meanwhile said on their website that Saudi fighter jets had bombed villages on the Yemeni side of the frontier on Tuesday, killing two women and wounding a child.
Strikes also targeted a government building in the village of Shida, they said.
In Tehran on Tuesday, Mr Mottaki was asked about Yemeni allegations that Iranian religious and media organisations were backing the rebels, who want more autonomy and a greater role for their version of Shia Islam, Zaydism.
Last month, officials in Sanaa said security forces had seized a ship carrying weapons destined for the Houthis at a port in Haja province, and detained its crew. Iranian officials dismissed the story as a fabrication.
"A country which seeks a role to establish peace and stability in all countries in the region... cannot have a role in creating tensions," Mr Mottaki said.
"We strongly warn the regional countries to be careful, to be vigilant," he added.
"Monetary aid, providing arms to extremist and terrorist groups or actually taking action against them and crushing those groups or the people and embarking on military operations - these all will have negative consequences."
In an apparent reference to Saudi Arabia, with whom Tehran has had hostile relations since the 1979 Islamic Revolution, Mr Mottaki said there were "certain people who add fuel to some crises".
"Those people should be assured that the smoke and the fire they have ignited will entangle them themselves," he added.
The minister said regional powers should instead try to restore stability in Yemen.
"Any kind of instability in Yemen, any kind of instability in Iraq, in Afghanistan or in Pakistan, they will have their own impact on the whole region," he warned.
Later, a commander of the militant group, al-Qaeda in the Arabian Peninsula, purportedly urged Sunnis to confront the Houthis.
In an audio recording posted on the internet, Mohammed Bin Abdul Rahman al-Rashid, denounced what he called the Yemeni rebels' aspirations and incursions against Sunnis.
He said the Shia community and Iran were trying to take over Muslim countries, and that "their threat to Islam and its people is much bigger than that from Jews and Christians".
The Yemeni government launched a fresh offensive in August 2009
The Houthis, named after the family of their leader, say they are trying to reverse political, economic and religious marginalisation of their community.
They also accuse Saudi Arabia of supporting the Yemeni armed forces by allowing them to launch attacks from its territory, a charge both countries deny.
The Yemeni government accuses the rebels of wanting to re-establish Zaydi clerical rule, which ended in 1962, and of receiving support from abroad.
The Zaydi community are a minority in Yemen, but make up the majority in the north of the country.
The insurgents first took up arms against the government in 2004, after which government forces killed or captured much of the Houthi leadership.
The government launched a fresh offensive in August 2009, which has precipitated a new wave of intense fighting.
Aid agencies say tens of thousands of people have been displaced.