The powerful bombing heard across Kabul also left 24 people wounded, though it was not immediately clear if the embassy was the intended target.
No group has so far claimed responsibility for the attack, which comes just two days after a second round of a four-country meeting in Kabul aimed at reviving talks with the Taliban.
"A suicide attacker rammed into a civilian minibus on Darul Aman road and there have been casualties," Kabul deputy police chief Sayed Gul Agha Rohani.
Car bomb explodes near Russian embassy in Kabul, casualties feared
The interior ministry, which earlier reported that the explosion was caused by a suicide bomber, said the bombing left four people dead and 24 others wounded.
The road links downtown Kabul to the historic war-damaged Darulaman Palace, built by Afghan King Amanullah Khan.
The loud explosion sent a plume of smoke rising in the sky, with ambulances and firefighters rushing to the scene which was littered with charred debris.
Delegates from Afghanistan, Pakistan, China and the United States convened in the Afghan capital on Monday for a one-day meeting seeking a negotiated end to the 14-year Taliban insurgency.
Afghan Taliban urged to join reconciliation process
The first round of the so-called "roadmap" talks was held in Islamabad last week as the four nations try to lay the groundwork for direct dialogue between Kabul and the extremist group.
Taliban representatives were notably absent in both rounds and analysts caution that any substantive talks are still a long way off.
The Taliban has stepped up attacks on government and foreign targets in Afghanistan this winter, when fighting usually abates, underscoring a worsening security situation.
Observers say the intensifying insurgency highlights a push by the militants to seize more territory in an attempt to wrangle greater concessions during talks.
Afghan Taliban flex muscles with new telecom 'tax'
At last week's talks in Islamabad an Afghan government spokesperson said Pakistan would unveil a list of Taliban members who are ready for talks, but no names have so far been released.
Pakistan hosted a milestone first round of talks directly with the Taliban in July.
But the negotiations stalled when the insurgents belatedly confirmed the death of longtime leader Mullah Omar, sparking infighting within the group.
Afghanistan sees the support of Pakistan as vital to bring the Taliban to the negotiating table.
The four-country group is set to hold the next round of discussions on February 6 in Islamabad.
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