 "Heavy casualties as Taliban suicide bombing rattles Kabul")
The Taliban claimed responsibility for the attack near government offices, which sent clouds of acrid smoke billowing in the sky and rattled windows several kilometres (miles) away.
The brazen assault in a densely packed neighbourhood marks the first major Taliban attack in the Afghan capital since the insurgents announced the start of this year's fighting season.
"(We) condemn in the strongest terms the terrorist attack in Puli Mahmood Khan neighbourhood of Kabul, as a result of which many of our countrymen were martyred and wounded," Ghani said in a statement without specifying the number.
The Afghan health ministry said at least 208 wounded people were rushed to hospital but did not specify any fatalities.
"Such cowardly terrorist attacks will not weaken the will and determination of Afghan security forces to fight against terrorism," Ghani said.
Taliban spokesman Zabihullah Mujahid claimed their fighters had managed to enter the offices of the National Directorate of Security, the main spy agency.
Afghan officials did not confirm that claim but intense gun battles could be heard near the NDS compound. The Taliban are generally known to exaggerate battlefield claims.
"The first blast was carried out by a suicide bomber in a car and possibly one or two bombers are still resisting," interior ministry spokesman Sediq Sediqqi told AFP.
"The scene of the attack has been completely cordoned off by Afghan security forces."
The Taliban today last week announced the start of their "spring offensive" even as the government in Kabul seeks to bring them back to the negotiating table to end the drawn-out conflict.
The Taliban warned they would "employ large-scale attacks on enemy positions across the country" during the offensive dubbed Operation Omari in honour of the movement's late founder Mullah Omar, whose death was announced last year.
The insurgents began the fighting season last week by targeting the northern city of Kunduz, which they briefly captured last year in a stunning setback for Afghan forces.
But officials said Afghan security forces drove Taliban fighters back from the city on Friday.