President Hamid Karzai issued a statement condemning the attacks and seemingly putting some of the blame on NATO forces, The New York Times reported.
A total of four civilians were reported from the attacks -- two in Paktia Province, one in Jalalabad and one in Kabul -- while dozens more were injured and at least eight Afghan National Security forces members died.
Karzai called for an investigation into what he called an "intelligence failure for us and especially NATO."
The British government, a target of attacks in Kabul, said it condemned coordinated attacks on the city but lauded the response from Afghan security forces.
Heavy weekend fighting spilled over into Monday as Taliban militants announced the start of a spring offensive with coordinated attacks on targets in Kabul, including the British Embassy and the building housing the Afghan Parliament.
British Foreign Minister William Hague said there were few reports of serious injury and damage to the premises was minimal.
"The Afghan National Security Forces responded to the attacks bravely, promptly and effectively, once again illustrating the significant progress that has been made in ensuring that Afghans can look after their own security," he said in a statement. "Britain stands with the government and people of Afghanistan as they work to build a peaceful future."
British forces in Afghanistan recently handed over parts of Helmand province over to their Afghan counterparts. Afghan forces are set to take control over security beginning in 2014.
The attack on Kabul ended Monday, roughly 18 hours after it began. The Guardian newspaper in London reported that elite forces had outmaneuvered insurgents in one of the most serious attacks on Kabul since the Taliban government was overthrown in 2001.