Both attacks struck central Afghanistan, not far from the heavily secured capital Kabul, and were claimed by the militia leading a nearly 10-year insurgency against US-led NATO troops and the Afghan government.
In the first attack, an attacker drove a car laden with explosives towards a government building in Mahmud Raqi, capital Kapisa province northeast of Kabul. The government said the driver blew himself up when he was stopped at a nearby checkpoint.
The interior ministry said in a statement: "At around 10:00am (1100 IST), a suicide car bomb attack was carried out.
As a result, five civilians and two policemen were martyred and one policeman and three civilians were injured." Taliban spokesman Zabiullah Mujahid said it had carried out the attack which he claimed had targeted the French ambassador to Afghanistan and French soldiers who were visiting the governor's office at the time.
The French ambassador to Kabul told AFP he was 15 minutes away when the attack happened and that his impending visit had been publicly known.
"I had a meeting this morning with the government then with all the Kapisa deputies. At the moment, I have nothing that allows me to think I was targeted," Bernard Bajolet told AFP.
"My visit was known because all the deputies of Kapisa were involved." Lieutenant Colonel Eric de la Presle, a spokesman for the French contingent based in Kapisa, said no French soldier had been present at the time of attack.