"The war is widened," said South Sudan Information Minister Barnaba Marial Benjamin. "The battle is raging. It is spreading all over."
The U.S. State Department's Nuland said it is critical that leaders in both countries immediately exercise maximum restraint.
Britain's Minister for Africa, Henry Bellingham, said the "cycle of provocative and irresponsible acts" by both militaries must end immediately. He called South Sudan's move into Heglig "completely unacceptable."
"I call on both sides to establish a ceasefire and withdraw all forces immediately from one another's territory," he said.
The continued clashes have dimmed hopes for a resolution between the two countries on a host of issues left over from their July split, including oil-sharing, citizenship issues and the demarcation of the border.
Sudan President Omar al-Bashir was scheduled to visit South Sudan for a summit April 3, but the talks were scrapped in the wake of the clashes.
President Barack Obama earlier this month called South Sudan President Salva Kiir to ensure that South Sudan's military exercises maximum restraint and is not involved in or supporting fighting along the border.
In New York on Wednesday, the U.N. Security Council discussed its peacekeeping mission in Abyei, to the west of the current conflict.
Saeed reported from Khartoum. Associated Press Writer Peter James Spielmann contributed to this story from the United Nations.