He said he was awakened by the explosions and car bombing. He and his family were not hurt, but a woman from a neighboring house was hit by a stray bullet, he said.
An Associated Press reporter at the scene said that during the fight a number of large explosions could be heard inside and around the building, along with heavy gunfire.
On Wednesday, six Taliban suicide bombers attacked the gates of the Afghan intelligence service in downtown Kabul, killing one guard and wounding dozens. That operation bore several similarities to Monday's attack, including the use of a secondary car bomb placed outside the government compound.
The attacks occurred despite the Afghan government's push to get the Taliban to the negotiating table and as President Hamid Karzai and the U.S. negotiate for a quicker pullout of American forces.
After a meeting with Karzai earlier this month in Washington, President Barack Obama said the U.S.-led military coalition would hand over the lead for security around the country to Afghan forces this spring — months ahead of schedule. Obama also said he agreed with Karzai that the Taliban should open a political office in Qatar to facilitate peace talks.
Moreover, Pakistan, a powerbroker in the region, said last week that it plans to release more Afghan militant detainees before international troops finish their drawdown in Afghanistan at the end of 2014. Islamabad made the announcement after talks with Afghan and U.S. officials in Abu Dhabi, the capital of the United Arab Emirates. Pakistan is thought to be holding more than 100 Taliban prisoners and has so far released 26.
Kabul has pressed hard for Pakistan to release Afghan detainees, with some officials saying that they hope the released Taliban can serve as intermediaries to help prospective talks gain traction. But Washington is worried that some of the detainees might rejoin the fight if released.
Associated Press writers Rahim Faiez and Heidi Vogt contributed to this report.