Sudanese men caught attempting to 'illegally cross' Israeli border
A military spokeswoman told AFP it was believed the men had intended to seek work in Israel, which was home to more than 6,000 Sudanese asylum seekers as of January.
The Lebanese army said it had detained "five Sudanese people" near the Israel border for their illegal presence there and was investigating them.
Israel and Lebanon are technically at war, with the Jewish state having fought a full-fledged war against Hezbollah, the Iran-back Lebanese militia, in 2006.
Israel also remains technically at war with Sudan, which supported hardline Islamists - including, for a period, Al-Qaeda - under former president Omar al-Bashir.
In February, Israel's Prime Minister Benjamin Netanyahu and Sudan's leader, Abdel Fattah Al-Burhan, met in Uganda for what the Israeli prime minister's office described as talks aimed at normalising ties.
The controversial meeting led to an Israeli aircraft flying through Sudanese airspace for the first time, in what Netanyahu called another example of warming ties between the two formally hostile states.
"The first Israeli airplane passed yesterday over the skies of Sudan. This is quite a change," Netanyahu told American Jewish leaders in Jerusalem in February, without offering further details.
Israeli daily Haaretz quoted an Israeli government official, speaking on condition of anonymity, saying that the plane was "a private Israeli executive jet".
Sudanese protesters gathered in the capital Khartoum to denounce what was described as "normalisation with the Zionist entity" after reports of the secret meeting surfaced.
A Sudanese government spokesman at the time quickly scrambled to tame public outrage, saying Burhan "did not give a promise of normalising or having diplomatic relations".
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However, Sudan's military head of state said Israel has a key role to play in removing the country from a US blacklist for state sponsors of terror, in comments to Arab newspaper Asharq Al-Awsat just days after the controversial meeting.
Sudan has been part of a decades-old Arab boycott of Israel over its treatment of the Palestinians and its occupation of Arab lands.
Egypt and Jordan are so far the only Arab states to have full diplomatic relations with Israel.
Netanyahu visited Oman in 2018, and frequently says the boycott of his country is ending, despite the absence of a peace deal with the Palestinians.