The White House said Monday there was no deal on a prisoner swap with Iran at this time, despite repeated claims by Tehran that an agreement has been reached.

But the White House also said that the United States is continuing to engage with Iran over how to get home Americans unjustly detained there.

"There's no deal. And the last thing that we want to do is give false hope to families that have been waiting for a long time for their loved ones to come home," White House national security adviser Jake Sullivan told reporters.

The Iranian foreign ministry once again said earlier Monday that a "written agreement has been signed by the official representative of the United States” though it did not specify who.

Three US dual nationals and possibly two permanent residents are held by Iran in what human rights organizations call hostage diplomacy by the Islamic Republic.

Tehran, which lost the chance to conclude a nuclear deal with the US and its European allies last September, has been repeatedly claiming that a prisoner release is imminent. It is believed that in case of an agreement over the hostages, the US would agree to the release at least $7 billion in Iran’s frozen funds held in South Korea.

It would be a politically difficult decision by the Biden administration to hand over money to the Iranian regime at a time when Tehran is supplying weapons to Russia and violently suppressing its own people.