A mortar shell was fired overnight in the direction of the French embassy in Yemen, while a car bomb exploded metres away in Sanaa's diplomatic quarter, a police source said Monday.

"The two attacks happened after midnight. There were no victims," the source said.

The shell fell by a concrete block, installed for security reasons on a road leading to the embassy, he added.

That blast came shortly after a car exploded on the nearby main road.

"The shell landed about thirty metres (yards) from the wall of the French embassy," while the car "was parked halfway between the embassy and the residence of former president Ali Abdullah Saleh in the capital's diplomatic district of Hadda, the same source said.

Those explosions came shortly after two devices went off in a minibus parked in the centre of Sanaa not far from the defence ministry, also causing no casualties, a military source told AFP.

Such violent acts have increased in Yemen where Shiite Huthi rebels have been pushing out from the mountains of the far north to areas closer to Sanaa to expand their hoped-for autonomous unit in a promised federal Yemen.

That prospect of a federal Yemen was originally mooted as a way to address grievances of the formerly independent south, where tensions are high as secessionist violence rises.

Al-Qaeda militants have also seized foreigners in the poor country which is undergoing a difficult transition since nationwide Arab Spring protests that forced Saleh to step down in February 2012 after 33 years in power.

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