The blockade has led to shortages of fuel and food ahead of next week's Muslim holiday of Eid.
The death toll is unclear but sources say between 30 and 50 people died in Wednesday’s attacks.
Former Defence Minister Sadio Camara was killed in a massive offensive by combined jihadist and separatist forces.
The blockade comes days after Mali's defence minister was assassinated in a series of nationwide attacks.
The UK has issued similar advice, telling citizens who stay, that they do so at their own risk.
Last weekend's attacks came as the Africa Corps withdrew from a key base in northern Mali.
The military came to power to bolster security but the weekend's attacks have brought that into question.
Ethnic Tuareg fighters say they are in control of Kidal following a weekend of nationwide attacks, alongside Islamist groups.
A wave of coordinated attacks by jihadist militants and separatists has spread through the country.
