The response was carried on the Somali Memo website which is affiliated to the al-Qaeda-linked group.
On Thursday, President Farmajo offered the militants an amnesty at the same time as declaring war on the group.
The UN-backed government in Mogadishu has been fighting the militants for control of Somalia for nearly a decade.
Mr Farmajo promised that fighters who gave themselves up within 60 days would get training, employment and education.
The president's statement was made "just to please the West", an al-Shabab official is quoted as saying.
Mr Farmajo announced the amnesty at a news conference in the capital, Mogadishu, dressed in full military fatigues.
"We want to pardon the Somali youth who were misled by al-Shabab," he said.
He also announced a major shakeup in the drought-stricken country's security services.
Senior officers in Somalia's intelligence service and police force have been replaced to prepare for the escalating war against the militants.
Mr Farmajo named a new military commander, director of national security and intelligence, commander of police and a new head of prison forces.
The new president was elected in February promising a "new beginning" for the country.
Somali Islamist militant group al-Shabab has dismissed President Mohamed Abdullahi Faramajo's declaration of war.