Czech chief of staff Petr Pavel told reporters in Prague that the bomber was in a crowd of Afghans talking to soldiers who were investigating rocket attacks against the Bagram airbase, a major US military facility nearby.
The attack, which was claimed by the Taliban, comes as Afghanistan is mired in a political crisis, with a bitter row raging over allegations of fraud in the presidential run-off election.
Waheed Sediqqi, spokesperson for the governor of Parwan province, told AFP that ten civilians and two policemen were killed in the attack as well as the four soldiers.
The Taliban claimed 15 US special forces soldiers were killed. They routinely make exaggerated claims after such attacks.
About 250 Czech soldiers serve among the 50,000 US-led Nato troops still deployed in Afghanistan.
Nato's combat mission will wrap up at the end of this year, with 10,000 US troops staying into next year if the new president signs a security deal with Washington.
About 3,450 coalition troops have been killed in Afghanistan since operations began in 2001 when the Taliban regime was ousted from power.
The attacks came as US Secretary of State John Kerry warned Tuesday that any attempt to seize power in the election crisis would cost the country its international aid.
Initial results released on Monday showed former World Bank economist Ashraf Ghani had won the election, but a spokesperson for his poll rival Abdullah Abdullah rejected the outcome as "a coup against the will of the people".
Fraud allegations immediately stoked concerns of instability after the figures showed Ghani collected 56.4% of the run-off vote against ex-foreign minister Abdullah's 43.5%.
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