Libya has accused Sudan of flying weapons to "terrorist" groups on its territory and declared Khartoum's military attache persona non grata, a government statement said.
Khartoum denied the allegation and said it had received no formal notice of the attache's expulsion.
According to the Libyan statement, received on Sunday by AFP, a Sudanese aircraft carrying ammunition destined for Libyan armed groups landed in the southern Kufra region on an unspecified date.
The government said the plane had violated its airspace and made an unauthorised landing, describing this as "an attack on (Libya's) national sovereignty".
It accused Sudan of interfering in Libyan affairs and "backing terrorist armed groups".
The Libyan government declared the Sudanese military attache in Tripoli persona non grata and said he must leave the country and return home.
It said that the plane, after landing in Kufra to refuel, headed for Miitiga military airport in Tripoli which is held by mostly Islamist militiamen.
The militiamen effectively seized control of the capital last month after fierce clashes with nationalist fighters.
The statement did not say when the incident took place or if the plane actually touched down in Miitiga.
"Sudan has no interest to intervene in the internal Libyan affairs," the official SUNA news agency said, citing Khartoum's foreign ministry.
The plane which landed at Kufra last Friday was on a routine mission to supply "the joint Sudanese-Libya forces" who control the border with food and ammunition, ministry spokesman Yousif Al-Kordofani said.
He added that the aircraft did not head toward Miitiga, and Sudan "did not receive any call" from Libyan authorities calling for the withdrawal of the military attache.
Libya has been sliding into political and security chaos since dictator Moamer Kadhafi was overthrown and killed three years ago.
The interim authorities are confronting powerful militias which fought to oust Kadhafi, and are also split in parliament and in the government.
The internationally recognised government of prime minister Abdullah al-Thani has been meeting for security reasons in the eastern city of Tobruk. On Monday it said armed groups were in control of ministries and blocking access to government facilities in Tripoli.
On Tuesday a pro-Islamist figure, Omar al-Hassi, presented a rival cabinet lineup to the General National Congress, or parliament, in the capital.