Clashes have broken out between the armed forces of Sudan and South Sudan in several disputed border regions, both sides say.
A spokesman for the South Sudan army says it is the biggest confrontation since independence.
South Sudan seceded from Sudan last July after a long civil war. The nations have several outstanding issues, of which the biggest is oil.
Sudan state radio says President Bashir has now put off a visit to South Sudan.
He had been due to hold a summit next week with the President of South Sudan, Salva Kiir.
The clashes prompted President Kiir to warn of war.
He said: "This morning the [Sudanese] air force came and bombed... areas in Unity state.
"After this intensive bombardment our forces.... were attacked by the [Sudan Armed Forces] and militia."
Mr Kiir added: "It is a war that has been imposed on us again, but it is [Sudan] who are looking for it."
He said Southern forces had taken over the key oil field of Heglig, parts of which are claimed by both sides.
The South also reported Khartoum had attacked the disputed areas of Jau and Pan Akuach, and Teshwin inside South Sudan.
Sudan's army spokesman, Sawarmi Khalid Saad, confirmed fighting in the border area of Sudan's South Kordofan state and the southern Unity state, without giving the exact locations.
"The clashes there are still ongoing," he said.
In January, South Sudan shut down all of its oil fields in a row over the fees Sudan demands to transit the oil.
South Sudan depends on oil sales for 98% of state revenues, but pledged not to restart production until a deal was reached.
Parts of the countries' common border also remain in dispute.
In February, the two states agreed to demarcate most of the border within three months, although this would exclude five disputed areas.
Sudan: A country divided