People are dying from extreme heat, which is also killing a large number of chickens and destroying tea plants
The Russian foreign ministry said in a statement that they discussed "topical issues of the regional and bilateral agenda" during the meeting on Wednesday, according to news agency Tass.
However, Bangladesh foreign ministry has not issued any statement.
It has released the photos of the meeting, which took place amid the Rohingya crisis as over 430,000 Myanmar nationals from Rakhine State have taken refuge in Bangladesh following a military crackdown there.
The Security Council for the first time in nine years agreed a statement on Myanmar condemning the violence.
Lavrov is heading the Russian delegation to the session of the UN General Assembly, which opened on Sept 12.