Germany rejected Amri's asylum application last June, but Tunis denied he was a Tunisian citizen, blocking him from being sent home.
In response to failings which kept the suspected attacker at a Berlin Christmas market on December 19 from being deported to Tunisia before the carnage, German officials have threatened to end development aid.
"Europe must be calm. Tunisia is a country which assumes its responsibilities," Essebsi told AFP during a reception at the presidential palace.
"We have accords with Europe. We have bilateral accords with certain countries, including Germany. These are good accords that will be implemented, by them and by us," he said.
The president said Berlin had "identified... around a thousand Tunisians who are in Germany and do not have resident permits", whose identities had to be verified before repatriation.
"We cannot force any country to keep Tunisians whose status is irregular... but we must first ensure that they are indeed Tunisians, something which is not always the case."
Germany's Vice Chancellor Sigmar Gabriel warned in an interview with Der Spiegel magazine published last weekend: "Those who do not cooperate sufficiently (on repatriation) cannot hope to benefit from our development aid".
The warning was aimed in particular at Tunisia -- the home nation of Anis Amri, who was suspected of ploughing a lorry into the Berlin market killing 12 people.
Germany rejected Amri's asylum application last June, but Tunis intially denied he was a Tunisian citizen, blocking him from being sent home.
A new Tunisian travel document for the 24-year-old only arrived two days after the attack in Berlin.
Several thousand citizens of north African nations, including those with almost no chance of obtaining asylum in Germany, are similarly lacking papers to return home.
German authorities are now considering more routinely placing failed asylum seekers viewed as dangerous Islamists in detention ahead of their deportation.