The attackers' last two strongholds -- in the diplomatic enclave and near the parliament -- had been cleared, Interior Ministry spokesman Sediq Sediqqi told AFP.
"All attackers are dead, the fighting is over," he said.
Earlier, gunfire was heard as police launched an assault on a militant stronghold in the capital's diplomatic enclave in Wazir Akbar Khan.
Kabulwas hit by a wave of attacks in three areas Sunday, with embassies and foreign military bases coming under fire in what Taliban insurgents said was the start of their spring offensive.
Afghan security forces took the lead in countering the assault, but a spokesman for NATO forces in the country said they had provided air support in response to requests from the Afghans.
The US, British, German and Japanese embassy compounds came under fire as militants attacked the city's diplomatic enclave and tried to storm parliament, sparking a gun battle as lawmakers and bodyguards fired back from the rooftop.
Outside the capital, militants attacked government buildings in Logar province, the airport in Jalalabad, and a police facility in the town ofGardezin Paktya province, where a NATO helicopter was reportedly deployed against them.
The attacks raise fears over the precarious security situation inAfghanistanas NATO prepares to withdraw its 130,000 troops by the end of 2014 and hand responsibility for security to Afghan forces.
ButUSAmbassador Ryan Crocker said the ability of Afghan security forces to respond to the attacks was a "clear sign of progress".