The United Nations has expressed concern about the conflict on the border between Sudan and South Sudan. South Sudan gained access to much of the oil reserves in the region when it became an independent nation in July though Sudan governs the export infrastructure.
South Sudan's Information Minister Barnaba Marial Benjamin told al-Jazeera South Sudanese forces shot down the fighter jet.
"(T)here is concrete evidence of what we have been saying -- that we are under continuous attack from the Republic of Sudan, both by air as well as from the ground," he told the Arab broadcaster.
Sudanese officials described Juba's claims as baseless.
"No fighting took place today, and even when there were battles previously, the Sudanese army doesn't use planes, just artillery and that is after the South Sudanese army attacks first," said Sudanese military spokesman Col. Khaled Saad al-Sawarmi.
The 2005 peace deal that secured South Sudan's independence is threatened by border clashes, ethnic tensions and disputes over oil.