The minister told LRT Radio on Tuesday that the government was not planning to reintroduce border checks for people entering the country by car.
"That would mean (...) closing the borders again," she said. "Things are not so bad at the moment as to make us keep people under pressure and prevent them from travelling at least to a nearby country where the epidemiological situation is good".
The minister said it would be irrational to check travelers randomly without shutting the borders, because it would be too difficult to verify where people have actually arrived from.
"It's irrational to use our border forces for a thing like is," she said.
Tamasuniene expects returnees from countries with high infection rates to be responsible and self-isolate.
"We hope that we'll continue to have only isolated cases of imported infections," she said.
Health Minister Aurelijus Veryga warned on Monday that rising COVID-19 numbers in popular resorts where hundreds of Lithuanians are currently in now might cause a spike in coronavirus cases in Lithuania.
The epidemiological situation in Lithuania will depend on whether these travelers comply with the self-isolation requirement on return to the country, he said.
Lithuania has since June 1 registered 49 cases of coronavirus infection contracted abroad.
Lithuania's list of countries arrivals from which must self-isolate for 14 days currently consists of 63 countries.