Earlier this week, Israel approved a plan to force asylum seekers to choose between indefinite detention in an Israeli prison, or deportation to a third country in Africa.
The migrants were told they had three months to leave, drawing condemnation by activists who said the Israeli's government move would endanger people's lives.
Israel did not specify where the asylum seekers should go, but local media and rights groups have previously said that Rwanda and Uganda had agreed to take in migrants from Israel.
On Friday, however, Rwandan Foreign Minister Olivier Nduhungirehe said his country had not signed such a deal, calling the claims "fake news" in response to a Twitter post by Kenneth Roth, executive director of Human Rights Watch.
"Rwanda has no deal whatsoever with Israel to host any African migrant from that country," he said.
Okello Oryem, Uganda's foreign minister, has also denied the existence of such an agreement, calling any suggestion to the contrary "absolute rubbish".
"There is no written agreement or any form of agreement between the government of Uganda and the Israeli government to accept refugees from Israel," he was quoted as saying on Friday by news agencies.
'The infiltrators have a clear choice'
Currently, Israel is home to about 40,000 asylum seekers, according to government figures. That includes 27,500 Eritrean and 7,800 Sudanese asylum seekers, the UN refugee agency (UNHCR) has reported.
According to the Israeli scheme, asylum seekers will be given a plane ticket and up to $3,500 for leaving.
Speaking as the plan was approved by his cabinet on Wednesday, Israeli Prime Minister Benjamin Netanyahu said the move against asylum seekers - whom he referred to as "infiltrators" - would help Israel to "guard its borders".
"The infiltrators have a clear choice - cooperate with us and leave voluntarily, respectably, humanely and legally, or we will have to use other tools at our disposal, which are also according to the law," he said.
Most asylum seekers in Israel are from Sudan and Eritrea. They arrived in the country over the last decade via Egypt and most have fled war, torture and other mistreatment.
Between December 2013 and June of this year, about 4,000 Sudanese and Eritrean asylum seekers were deported under Israel's "voluntary departure programme" to Rwanda and Uganda, according to the UN's refugee agency (UNHCR).
In November, the UNHCR raised alarm that those who had already been relocated through that scheme were not receiving support after leaving Israel.
"UNHCR is concerned that these persons have not found adequate safety or a durable solution to their plight and that many have subsequently attempted dangerous onward movements within Africa or to Europe," it said in a statement.