Sudanese President Omar al-Bashir on Thursday vowed to teach "a lesson by force" to the South Sudanese government over its seizure of the north's main Heglig oil field.
Keeping up the war rhetoric that has sparked expressions of concern from the United States, Bashir dismissed talk by the United Nations that sanctions might be imposed on South Sudan.
"America will not invoke sanctions on them, and the (UN) Security Council will not, but the Sudanese people are going to punish them," declared Bashir, who holds the rank of field marshal and wore desert camouflage and a beret to address a rally of paramilitary troops.
On the battlefield, the Southern army repulsed ground attacks in recent hours in a widening conflict zone along the border, said the South's military spokesman Philip Aguer.
Ground assaults and air strikes were reported in the Heglig region, as well as the three Southern states of Unity, Western and Northern Bahr El-Ghazal, he said, adding that the Southern army was "still in its positions".
Sudan has vowed to reclaim Heglig "by hook or crook".
AFP reporters who have visited the Heglig battle zone along the disputed border say dead bodies and destroyed tanks are strewn around.
Southern troops are entrenched in positions around the area.
On Tuesday the UN Security Council discussed possible sanctions against both Sudan and South Sudan in a bid to halt a wider war after the fighting broke out on April 10.
Clashes escalated last week with waves of air strikes hitting the South, and Juba's seizure of the Heglig oil hub, which delt a huge blow to Khartoum's already faltering economy.
"We will teach them a lesson by force," Bashir said of the South Sudanese government. "Heglig is not the end. It is the beginning."
South Sudan's Information Minister Barnaba Marial Benjamin responded in Juba that his country is not at war with Sudan and is interested in peaceful relations.
"The Republic of South Sudan considers Sudan as a neighbour and friendly nation, not an enemy," Benjamin told reporters.
The United States on Wednesday voiced concern and called for an immediate halt to the fighting after Bashir threatened to topple South Sudan's "insect" government.
Bashir's remarks came on the same day that Princeton Lyman, the US special envoy on Sudan and South Sudan, visited Khartoum in an effort to ease tensions, and as China reiterated its concern over the escalating conflict, calling for a resumption of dialogue.
South Sudan's President Salva Kiir is to hold talks with his Chinese counterpart Hu Jintao next week in Beijing, which has a vested interest in the oil industries of both nations.
Sudan's parliament has declared a "mobilisation and alert" of the population and this week voted unanimously to brand the South Sudanese government an enemy. Benjamin, the Southern minister, said the move amounted to a "declaration of war".
He has alleged Sudan was using Heglig as a base to launch attacks on his country.
Bashir, shouting and gesticulating with a traditional staff, spoke on Thursday in the North Kordofan capital El Obeid to hundreds of freshly trained members of the paramilitary Popular Defence Force, a mainstay of Sudan's fighting forces.
Some of the troops rode camels. They danced to martial music and shouted in praise of God.
The United Nations, the United States and the European Union have criticised the South's occupation of Heglig but have equally denounced Sudan's air strikes against the South.
There are widespread fears that the fighting will spread.
It is already the worst since South Sudan won independence in July after a 1983 to 2005 civil war which killed two million people.
Although South Sudan disputes it, Heglig has been internationally regarded as part of Sudan.
Sudan held talks on Wednesday with African Union chief Jean Ping and Ethiopian Prime Minister Meles Zenawi as part of its diplomatic efforts to pressure South Sudan into a pullout from Heglig.
Sudan's military has released virtually no information about the situation on the ground and the army spokesman did not answer his phone again on Thursday.
Since the invasion, production at Heglig has been shut and facilities there are leaking. The field accounted for about half of Sudan's oil, and its loss has worsened an economic crisis.
The International Monetary Fund on Wednesday forecast that Sudan's economy will shrink 7.3 percent this year, while consumer prices are expected to rise by an average of 23.2 percent.