Claims were made by Nusrat al-Islam wal Muslimeen, the Mali-based branch of al-Qaeda, on the "Telegram" channel of the group's so-called Al-Zallaqa Media Foundation, it said.
"Fighters mounted a surprise attack on the Malian army position in Soumpi, killing two soldiers and burning military vehicles as well as those belonging to Sogea-Satom," a French road construction company that the troops had been "guarding", it said.
A second communique reported attacks on gendarmerie posts in Dioro and Ouan in central Mali on Monday and a landmine blast on a Malian army vehicle in the Mopti region on Tuesday.
Groups of Islamic extremists linked to Al-Qaeda took control of the desert north of Mali in March and April 2012 at the expense of Tuareg rebels, but were chased out of Sahara towns by a French-led military operation launched in January 2013, which is still under way.
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Mali's army, French soldiers and a UN mission (MINUSMA) have no control of large tracts of the country, which regularly come under attack in spite of a peace accord signed with Tuareg leaders in May and June 2015, aimed at isolating the jihadists.
The creation of Nusrat al-Islam wal Muslimeen was announced on March 2 as a fusion of the groups Ansar Dine, the Al-Murabitoun of Mokhtar Belmokhtar and the "Emirate of the Sahara," a branch of a Al-Qaeda in the Islamic Maghreb (AQMI).