Rasnačs was criticized by opposition MPs about his poor oversight of insolvency administration, the abuse of which, foreign investors have pointed out, has cost Latvia hundreds of millions.
33 MPs supported the call for him to step down, while 41 was against and 9 'abstained'.
The no-confidence motion was paused last week as MPs attended memorial events for deportation victims.
"Here we're seeing an attempt to influence the makeup of the next Saeima," said MP Jānis Dombrava.
Nevertheless opposition MPs were seeking to topple the government, with Latvian Regional Alliance MP Juris Viļums saying the whole cabinet must step down.
Rasnačs, who was present at the Saeima meeting, invited MPs to the opening of a department dedicated to controlling insolvency processes on July 2. He also thanked cabinet members and the president for their support for ongoing reforms aiming to put an end to insolvency abuse.