Skvernelis' public disapproval rating rose by almost 9 percentage points in January to 38.6 percent, from 29.9 percent last month.
36.4 percent had a favorable opinion about the prime minister, down from 42.9 percent.
Meanwhle, Nauseda remains the most popular politician in Lithuania, having regained his November-level popularity rating of 73.6 percent, up from 69.3 percent in December.
7 percent had an unfavorable opinion about the president, down from 8.4 percent.
Vladas Gaidys, head of Vilmorus, says the rating changes have to do with the ongoing dispute between the president and prime minister over the transport minister, with Nauseda criticizing the minister and demanding his dismissal and Skvernelis voicing his support.
"It all comes to Skvernelis' prejudice," Gaidys told BNS.
The survey also showed that Foreign Minister Linas Linkevicius comes in second in the popularity rating after Nauseda, enjoying a popularity rating of 50.2 percent, compared to 50.7 percent in December.
He is followed by Speaker of the Seimas Viktoras Pranckietis with 47.7 percent (45.2 percent in December), and Kaunas Mayor Visvaldas Matijosaitis with 41.6 percent (40.7 percent).
The TOP-10 of most popular politicians in Lithuania also includes Defense Minister Raimundas Karoblis (32 percent), liberal MP Viktorija Cmilyte-Nielsen (29.6 percent), Education, Science and Sports Minister Algirdas Monkevicius (27.8 percent), Labor Party leader Viktor Uspaskich (27.8 percent) and Health Minister Aurelijus Veryga (26.9 percent).
On the other end of the spectrum, Narkevic is the most unpopular politician in the country, with only 7.5 percent having a positive opinion about him and 55.4 percent having a negative one, compared from 5.4 and 57.4 percent in December.
Vilmorus carried out the survey of 1,022 people on Jan 10-18.