The Social Democratic party (PSD) unexpectedly withdrew its support for Grindeanu on Wednesday, claiming he had failed to implement economic reforms in the European Union's second-poorest country.
But Grindeanu vowed Thursday that he would not step down until President Klaus Iohannis had appointed a successor from his Social Democratic party (PSD).
"Romania needs stability and responsibility," he wrote Thursday on Twitter while continuing with official business as usual, including a meeting with British Defence Minister Michael Fallon.
His defiant stance presents a conundrum for centre-right Iohannis, who under constitutional rules can nominate a new candidate only once the post has been vacated.
The move also infuriated the PSD, which called for a no-confidence vote that could take place next Wednesday.
"I had hoped that it wouldn't come to this and that Mr Grindeanu would respect democratic rules," said PSD head Liviu Dragnea after a meeting of about 60 party members Thursday in Bucharest.
But analysts say the standoff is the culmination of a power struggle between the 43-year-old premier and Dragnea, the powerful PSD head who had been hoping to lead the government himself.
The party boss, 54, was barred from running for premier because of a voter fraud conviction and is currently on trial for alleged abuse of power, a charge he denies.
Dragnea has made no secret of the fact that he had chosen Grindeanu as premier because he was a docile party loyalist.
But the prime minister has become increasingly rebellious, according to analysts.
"There's a clear difference between the Grindeanu who was appointed by Liviu Dragnea and the one who refused Wednesday to step down," political expert Ioan Stanomir told AFP.
"The only explanation for Grindeanu's elimination is Dragnea's wish to have absolute power inside the PSD and across the country," journalist Marian Sultanescu wrote on the independent news website Gandul.info.
'We're waiting'
The uncertain situation is the second major crisis to hit the PSD since it rode back into power in December, barely a year after being forced from office over a deadly nightclub blaze.
And in this case, the PSD has acknowledged that its hands are tied.
"We're waiting for Mr Grindeanu to resign," the party's general secretary, Codrin Stefanescu, told journalists in Bucharest on Thursday.
The party had been hoping to avoid calling a no-confidence vote -- and the political damage it could wreak on the party's image -- thanks to an intervention by the president.
But Iohannis appears to have ruled out naming a new premier while the post is still occupied.
"Mr Iohannis calls on the ruling coalition to quickly resolve this crisis to avoid a period of political instability," the president's spokeswoman Madalina Dobrovolschi said.
The standoff comes just months after Romania saw its largest protests since the fall of communism when the government tried to water down anti-corruption laws.
Analysts say Grindeanu's fall from favour could be linked to his perceived failure to push through the contested legislation, which could have allowed Dragnea to run despite his conviction.
"Liviu Dragnea only wants one thing -- amendments to the anti-corruption laws" that currently prevent him from becoming premier, according to former PSD member Alin Teodorescu.
The PSD was forced out in the wake of angry protests in 2015 over a nightclub fire in Bucharest that killed 64 people and was widely attributed to corrupt officials turning a blind eye to fire regulations.
A decade after joining the European Union, the former communist nation of 20 million inhabitants remains mired in poverty.
Nonetheless, Romania logged first-quarter economic growth of 5.7 percent, according to data released last month, the fastest rate in the EU.
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