The Government should publish a red-list of countries where travel should be banned, according to the Social Democrats.
Figures show more than 3,000 people flew from the United States to Ireland from the end of June to July 19.
Co-leader of the party, Catherine Murphy, said the issue of travel has been ignored by the Government for too long, and has called the inaction dangerous.
She believes banning flights from certain areas would help contain the spread of the virus.
Ms Murphy said: “There’s certainly locations in the world where the r-number is alarmingly high.
“I mean that was what the public concern was in relation to the United States where there were particular parts of the States where it was out of control or it was the epicentre.”
It comes as Mexico overtook the UK to record the third-highest number of deaths from coronavirus of any country in the world.
It has registered 46,688 fatalities during the pandemic so far, according to Johns Hopkins University.
It comes after the health ministry there announced a further 8,000 deaths.
The US still has the most number of Covid-19 cases and deaths in the world, 4,562, 170 cases and 153,314 deaths according to the tracker operated by Johns Hopkins University. Brazil is second.
Meanwhile, the number of new coronavirus cases in the Australian state of Victoria has gone down, but officials say they are still considering more restrictions.
There were almost 400 diagnoses and three deaths in the last 24 hours, compared to 627 cases and eight deaths the day before.
The state’s premier says the numbers are still too high and there’s a “growing case” for authorities to do more.
Elsewhere, Poland has reported its highest number of new coronavirus cases for a third day in a row with 658 people infected.
More than 200 cases were reported in the Silesia mining region which has been grappling with an outbreak among miners.
Five new deaths have also been reported and the prime minister hasn’t ruled out tightening some restrictions if the situation worsens.