Without directly mentioning the president's name, Skvernelis said that "for the past eight years, a position has been chosen to stand by and watch, evaluate and criticize, but basically do nothing".
Grybauskaitė in July will mark eight years since she was elected as president.
According to the prime minister, the reforms his government and the ruling majority are implementing are vital for Lithuania.
"Unless we want to continue lagging behind other civilized nations, at the very bottom, without any hope of rising. Unless we want to continue to do nothing but sigh hopelessly and throw up our hands because everything in the state is neglected and distorted, and nepotism, corruption, protectionism, double standards, mismanagement, inefficient management, illegal deals, alcoholism and a whole bunch of other ills flourish," he said in a Facebook post.
In Skvernelis' words, the current government and ruling coalition have launched reforms that had to be started two decades ago.
The prime minister said that the government maintained dialog with the public on all important issues.
"We are speaking and will continue to speak to people. We spoke to them while improving the Labor Code. People were represented in the Tripartite Council by trade unions, which approved the amendments to the code. We spoke and we are still speaking to the communities of all higher schools, and with the heads of forestry enterprises and forestry workers," he said.
Skvernelis described the chosen state forest management overhaul model as a compromise.
"The interests of forestry workers are protected (...). They face no layoffs. On the contrary, it is planned to raise their wages. But we can no longer tolerate the mismanagement and arbitrariness in 42 separate (forestry enterprises)," he wrote.
According to the prime minister, the current higher education network is falling apart.
"Such a hopeless situation, where the higher education system serves only itself, rather than for the future of society, where universities are forced to think about how to survive in a 'wild market', is due to the inaction and indecisiveness of all those who have governed the country until now. If timely decisions had been made, we would not have to try and desperately solve the situation now," he said.
"It is with people who have been engaged in non-transparent activities and profited from this for years that dialog is really impossible and makes no sense," the prime minister said.
"We are not surprised to see resistance to reforms from these people, but they are not going to stop us," he added.
President Grybauskaitė several hours earlier accused the government of "political arrogance" in carrying out reforms and called for the new Labor Code to be improved in workers' favor.