A no-confidence vote is expected to fail as Grindeanu's left-wing Social Democrat party (PSD) holds a solid majority.
The motion, tabled by the centre-right opposition, is expected to fail as Grindeanu's left-wing Social Democrat party (PSD) holds a solid majority.
"Romanians don't want corrupt politicians to be pardoned and shielded from justice. We call on you to stop acting against the law," read the motion filed by 123 opposition MPs.
On Tuesday, the prime minister remained defiant in the face of Romania's largest protests since the fall of communism in 1989.
Calling for "calm and stability", Grindeanu insisted he would not resign.
For more than a week, hundreds of thousands of people have been taking part in demonstrations against an emergency decree approved on January 31, which critics say would have protected the corrupt from prosecution.
Although the decree was scrapped late Sunday, the marches have continued, with some protesters vowing not to stop until the government steps down.
While the crowds have noticeably shrunk from the half a million people thronging cities and towns on Sunday, they are expected to grow again over the weekend.
"Every action the government took in the last week proves that they are not honest at all. So we cannot trust them," protester Danchiric, who works in advertising, told AFP at Bucharest's Victory Square on Tuesday night.
Earlier in the day, the opposition-backed President Klaus Iohannis had hinted that the government should quit.
"The repeal of the decree and the possible sacking of a minister is too little. Early elections are too much," Iohannis told MPs in Bucharest.
Instead, he said, the onus was now on the Social Democrats to find a solution.
"If the PSD, which has created this crisis, fails to resolve the crisis immediately, I will summon all the political parties for talks," the president warned.
"You've won, now govern and legislate -- but not at any price."
The government still also aims, via a separate decree to be reviewed by parliament, to free some 2,500 people serving prison sentences of less than five years.
Grindeanu has argued the measures were meant to bring penal law into line with the constitution in the European Union member and reduce overcrowding in prisons.
But critics see the moves as a brazen attempt to let off the many lawmakers who have been ensnared in a major anti-corruption drive in recent years, as Romania seeks to shed its reputation as one of the bloc's most graft-riddled countries.
That push has seen almost 2,000 people convicted for abuse of power and a serving prime minister and a string of ministers and lawmakers go on trial.
The government's latest manoeuvres set alarm bells ringing in Brussels. The European Commission, which had previously praised Romania for its efforts, warned against "backtracking".
Washington also said it was "deeply concerned" about "accountability" for corruption crimes.