Operation Mansouri - named after the group's former leader, killed in a USA drone strike in 2016 - will target foreign forces with "conventional attacks, guerrilla warfare, complex martyrdom attacks, insider attacks", an insurgent statement said.
This week Afghan authorities arrested 35 soldiers who served on an army base in northern Afghanistan where the Taliban staged a deadly attack last week as fears grew they had inside help. There was no reference to any potential peace talks with the government.
Fighting has been fierce as USA and Afghan special operations forces, backed by hundreds of air strikes, have sought to advance against militant strongholds in recent months.
Ahmadi said the offensive would be a mix of conventional, guerrilla and suicide attacks on Afghan and foreign forces, underlining the challenges facing the United States administration as it weighs its options in Afghanistan. Afghanistan's defense minister and army chief of staff both resigned from their positions following the incident. In an emailed statement the Taliban also claimed the district, while Badakhshan's deputy governor Mohammad Bidar said fighting between Afghan Security Forces and the Taliban was still intense in the area.More news: Princess Charlotte about to turn 2; new photo released
On Thursday evening the Islamic State group claimed on its website to have repelled an attack conducted by American and Afghan forces and to have caused USA casualties.
UNAMA documented a 54 percent increase in conflict-related deaths of women and a 17 percent rise in child fatalities compared to the same period a year ago.
Taliban spokesman Zabihullah Mujahid in an e-mailed statement on April 28 boasted that the militant group now controls more than half of the country, citing a USA report in February that said the Afghan government controls only 52 percent of Afghanistan's 407 districts.
The attackers all carried valid passes to the base, security sources told AFP, and were dressed in Afghan army uniforms.More news: Kanye West won't got to MET Gala with wife Kim Kardashian
The Taliban announcement of the offensive coincides with the anniversary of Afghanistan's so-called Saur Revolution against its pro-Russian rulers, which led to a 10-year uprising by USA backed Islamic insurgents, or mujahedeen, against an invading Soviet army.
"I believe this will be a hard year for Afghan security forces, as they will be facing the resilient Taliban's complex and sophisticated attacks countrywide", he told AFP.
As well as the Taliban, Afghanistan is also battling an emerging local affiliate of the Islamic State group known as Islamic State in Khorasan, which is an ancient name for a region that once included Afghanistan, Iran and parts of Central Asia.
The bombing triggered global shockwaves, but was criticised by observers who questioned its use against a group that is that is not considered as big a threat as the Taleban.More news: Corey Lee, SingleThread, and La Taqueria Win James Beard Nods
The incident comes just days after USA defence secretary Jim Mattis visited Afghanistan, and while U.S. troops are battling suspected Islamic State militants in Nangarhar province. The target was IS hideouts in the Achin district of Nangarhar province.